Q: Why was Jesus worshiped by the former blind man at John 9:38, and why did the Apostle Thomas refer to Jesus as my Lord and my God at John 20:28?

I don't believe in the Trinity because there is TOO MUCH evidence that proves that Jehovah and Jesus are two separate persons. Were the First Century Jews themselves confused at who Jesus is? Including the Apostles? And if they were not confused why was it not clarified in the Bible?
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A: According to the account in John chapter 9, Jesus gave sight to a man who had been blind from birth. This prompted the Pharisees to extensively question the man about his miraculous healing, and, being frustrated by his answers, they threw him out of the synagogue. According to the New Living Translation, this is what followed: “When Jesus heard what had happened, he found the man and asked, ‘Do you believe in the Son of Man?’ The man answered, ‘Who is he, sir? I want to believe in him.’ ‘You have seen him,’ Jesus said, ‘and he is speaking to you!’ ‘Yes, Lord, I believe!’ the man said. And he worshiped Jesus.” (John 9:35-38)

It says that the man worshiped Jesus. Most other Bible translations read similarly. For example, the King James Version says: “'And he said, Lord, I believe.’ And he worshipped him.” The New International Version reads: “Then the man said, ‘Lord, I believe,’ and he worshiped him.”

The Greek word used at John 9:38, and translated as "worshiped," is proseky’nesen (προσεκύνησεν) from prosky’nesis (προσκύνησις, ή). This word carries the idea "to do reverence to," and is variously translated in the King James Version as: bow down(1), bow down before(1), bowed down(1), bowed down before(2), bowing before(1), bowing down(1), prostrated himself before(1), worship(32), worshiped(17); (see The NIV Interlinear Greek-English New Testament). At John 9:38 most Bible Translations render that word as "worship," yet there are some exceptions. For example, the New World Translation says: "he did obeisance to him." The God's Word Bible reads: "The man bowed in front of Jesus." Young's Literal Translation reads similarly: "and bowed before him." The Darby Translation puts it this way: "And he said, I believe, Lord: and he did him homage."

He "did obeisance to him," “bowed in front of,” or “he did him homage,” does not necessarily indicate worship of Jesus. Which Translations are more accurate in rendering the word "proskynesis"?

The NationMaster Encyclopedia says: Proskynesis, (Greek προσκύνησις) formed from the Ancient Greek words pros and kuneo literally means "kissing towards", and refers to the traditional Persian act of prostrating oneself before a person of higher social rank. . . According to Herodotus in his Histories, a person of equal rank received a kiss on the lips, someone of a slightly lower rank gave a kiss on the cheek, and someone of a very inferior social standing had to completely bow down to the other person before them.”

Let us look at other examples on how this word prosky’nesis is used in the Bible. At Matthew 9:18 the account relates, according to many Translations, “While He spoke these things to them, behold, a ruler came and worshiped Him, saying, ‘My daughter has just died, but come and lay Your hand on her and she will live.’" —New King James Version

Here The NIV Interlinear Greek-English New Testament renders the word proseky’ne (προσεκύνει) as “worshipped” in the Interlinear column directly under the Greek word, but translates it as “knelt before him” in the left column: “While he was saying this, a ruler came and knelt before him and said, ‘My daughter has just died. But come and put your hand on her, and she will live.’" The New World Translations says the man "began to do obeisance to him."

The parallel account in Luke gives a clearer picture of what took place on that occasion. According to the New King James Version it reads: “And behold, there came a man named Jairus, and he was a ruler of the synagogue. And he fell down at Jesus’ feet and begged Him to come to his house.” (Luke 8:41) Luke does not use the word prosekyne to describe what the man did, as does Matthew, but he simply states that Jairus fell down at the feet of Jesus (πεσών παρά τούς πόδας ΄Ιησού).

There is not the slightest indication that Jairus, “a ruler of the synagogue,” fell down before Jesus in order to worship him. He simply “knelt” before Jesus, or “fell down at [his] feet,” in order to implore him for help or mercy. This is very similar to what the slave did in Jesus' illustration at Matthew 18:26. There the slave, who owed his master a huge amount of money (ten thousand talents), which he could not possibly repay, fell on his knees before his master and pleaded for mercy. Matthew uses the word prosekyne to describe the action of the slave, which, interestingly The NIV Interlinear Greek-English New Testament translates as did obeisance under the Greek word, and renders as "fell on his knees" in the left column. Most other Bible Translations agree that the slave did not "prostrate" (NASB) himself before his master in order to worship him. The exception is the King James Version which translates "prosekyne" here as "worship," although the New King James Version reads it as he "fell down before him," while the 21st Century King James Version says he "fell down and did homage to him."
 

At Matthew 8:2 you will find another example of how the word prosekyne is translated in various Bible versions as: “worshiped” (New King James Version, American Standard); “bowed down before him” (NASB, New Century Version); “knelt before him” (New Living Translation, English Standard, New International Version - UK); “got down on his knees in front of” (New International Reader's Version); “prostrating himself, worshiped him” (Amplified Bible); "doing obeisance" (Kingdom Interlinear Translation).

It's interesting what the Catholic Encyclopedia (1913) says regarding the word “proskynesis,” usually translated as "worship":
 

Anastasius, Bishop of Theopolis (d. 609), who was a friend of St. Gregory and translated his "Regula pastoralis" into Greek, . . .makes the distinction between proskynesis and latreia that became so famous in Iconoclast times: "We worship (proskynoumen) men and the holy angels; we do not adore (latreuomen) them. Moses says: Thou shalt worship thy God and Him only shalt thou adore. Behold, before the word 'adore' he puts 'only', but not before the word 'worship', because it is lawful to worship [creatures], since worship is only giving special honour (times emphasis), but it is not lawful to adore them nor by any means to give them prayers of adoration (proseuxasthai)" (Schwarzlose, op. cit., 24).

So in English by adoration we now always understand the latreia of the Fathers of the Second Nicaean Council. From this adoration the council distinguishes respect and honourable reverence (aspasmos kai timetike proskynesis) such as may be paid to any venerable or great person-the emperor, patriarch, and so on. A fortiori may and should such reverence be paid to the saints who reign with God. The words proskynesis (as distinct from latreia) and douleia became the technical ones for this inferior honour. Proskynesis (which oddly enough means etymologically the same thing as adoratio -- ad + os, kynein, to kiss) corresponds in Christian use to the Latin veneratio; douleia would generally be translated cultus. In English we use veneration, reverence, cult, worship for these ideas. —Wikisource: Catholic Encyclopedia (1913)/Veneration of Images. (Bold added to highlight points)

According to the above Encyclopedia, we may “worship men and the holy angels,” because worship is “only giving special honour,” or "respect and honourable reverence, such as may be paid to any venerable or great person." In that sense it can be said that some worshiped Jesus, they knelt before him (went to their knees), bowing to him, and did him homage (obeisance), for he was certainly worthy of special honor, the greatest man who ever lived, “the Son of Man.” Yes, God’s Son.

As to your second question: “Why did the Apostle Thomas refer to Jesus as my Lord and my God at John 20:28,” I can only say that the apostle John recorded what the apostle Thomas had said. That certainly does not prove that Jesus is God, the Father of Jesus, nor that Thomas even implied that he believed it, just as you note, “there is TOO MUCH evidence that proves that Jehovah and Jesus are two separate persons.”

Perhaps we can look at a couple of examples to understand what Thomas might have meant. When Jacob wrestled with an angel all night, and had his name changed to Israel, meaning “contender with God,” it says that “Jacob called the name of the place Peniel [the face of God], saying, For I have seen God face to face, and my life is spared and not snatched away.” (Genesis 32:28-30; Amplified Bible)

Did Jacob believe that he had actually seen God face to face, even grappling with him all night? Perhaps, what he said to his brother Esau, when overcome with emotion and trembling at meeting him after many years apart, sheds light on what he meant, “for truly to see your face is to me as if I had seen the face of God, and you have received me favorably.” (Genesis 33:10; Amplified Bible)

Consider another example at Judges 13:21,22: “The angel did not appear again to Manoah and his wife. Manoah finally realized it was the angel of the Lord, and he said to his wife, “We will certainly die, for we have seen God!” Why did Manoah say that he had "seen God," even though he realized "it was the angel of the Lord"? He certainly did not mean that the angel was God himself.

Did any of the apostles believe that Jesus was God himself? When Jesus asked his disciples: “You, though, who do you say I am?” what did they reply? Simon Peter answered, perhaps in behalf of them all: “You are the Christ, the Son of the living God.” (Matt. 16:13-17) Jesus assured them that his “Father who is in heaven” had revealed this to them. Would Thomas also have understood that? The apostle John definitely states that "No one has seen God at any time." (John 1:18, King James Version)

I hope this also answers the other part to your question, whether or not the apostles were confused about who Jesus was. The confusion only came after the last of the apostles had died after the end of the first century. There is no ambiguity in the Scriptures about Jesus' identity and his relationship with his Father Jehovah God. This is clearly explained by Paul at Hebrews 1:1-6 (New Century Version):

“In the past God spoke to our ancestors through the prophets many times and in many different ways. 2 But now in these last days God has spoken to us through his Son. God has chosen his Son to own all things, and through him he made the world. 3 The Son reflects the glory of God and shows exactly what God is like. He holds everything together with his powerful word. When the Son made people clean from their sins, he sat down at the right side of God, the Great One in heaven. 4 The Son became much greater than the angels, and God gave him a name that is much greater than theirs. 5 This is because God never said to any of the angels, 'You are my Son. Today I have become your Father.' [Psalm 2:7] Nor did God say of any angel, 'I will be his Father, and he will be my Son.' [2 Samuel 7:14] 6 And when God brings his firstborn Son into the world, he says, 'Let all God's angels worship (proskynesis) him. [Psalm 97:7].'"

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