I am confused as to what is the correct day of "Sabbath". I've been celebrating worship/going to Church on Sunday all my life. The
controversy confuses me and I would like to KNOW THE TRUTH!!!!!!
Please provide Scripture if you can, help with this.

The Sabbath day is the seventh day of the week which is our Saturday. In Genesis 2:2,3 we note that God rested on the seventh day from all his work
which he had made. And God blessed the seventh day, and sanctified it: because that in it he had rested from all his work which God created and made. Until Christ died on the cross the children of God were to remember the Sabbath Day and keep it holy, but after his death and resurrection and with the advent of Christianity the day of worship was changed to first day of the week. The first day of the week is referred to as the Lord's Day in Revelation 1:10. 

In Acts 20:7 we note the early church came together on the first day of the week to break bread (partake of the Lord's Supper), and in 1 Corinthians 16:1,2 we see the church coming together on the first day of the week. Christ rose from the dead on the first day of the week and it was because of his resurrection that we have hope of our own resurrection.  Since he rose from the dead that day it is called the Lord's Day. Unlike the Sabbath it is not a day of rest, it is a day of worship and remembrance of our Lord's death and subsequent resurrection. 

The Jews all recognize that the Sabbath is Saturday and when one is in Israel on is acutely aware that Saturday is the Sabbath. When Jesus died on the cross he fulfilled the Law of Moses, and thus it is no longer to be observed. The old covenant which called for remembering the Sabbath Day and keeping it holy vanished, and the new covenant took its place (Hebrews 8:13). 

Is it necessary for a person to attend worship in order to be saved?

 Worship is extremely important in the life of the Christian.  By its very definition, to serve or honor one who is considered to have a state of value, shows its importance.  There are several reasons why one cannot be saved without worshiping God. 

1) Attendance at worship services was practiced by the early church, Acts 2:41-47 and Acts 20:7.  The book of 1 Corinthians deals with several problems related to worship.  The answer was not to quit worshiping but to correct the problems so that worship would be what it ought to be.  To neglect the worship services is to reject the pattern set by the early church.

2) To not attend the worship service prevents one from participating in some acts of worship designed for the assembly, such as giving and partaking of the Lord's Supper. 

3) To not attend the worship assembly is to violate the words of Jesus in John 4:23-24, "But the hour cometh and now is, when the true worshipers shall worship the Father in spirit and truth; for the Father seeketh such to worship Him.  God is a spirit, and they that worship Him must worship Him in spirit and truth. 

4) Not attending the worship assembly goes against the command to not forsake the assembling of the saints, Hebrews 10:25.  To not attend worship puts one in an unenviable position on judgment day.

If I study at home on Sundays and do not go to worship, will I be saved?

Only the Lord Jesus Christ will be the final judge as to whether one is saved or lost. However, there are things that God has commanded that will determine whether one is saved or lost. We must follow His will in all things. To deliberately absent oneself from the worship assembly goes against what He teaches in His word. 

1) The very definition of the word "church," of which a Christian is a part, implies that there is to be an assembling. Our English word "church" comes from the Greek word ecclesia, which means "the called out," "an assembly." 

2) We are absenting ourselves from the body of Christ of which we are a part. The Bible says in Acts 2:47 that those who were being saved were added to the church. The Bible says in Colossians 1:18 that Jesus is the head of the body, the church. 

3) We are not doing the very thing the early church did. Acts 2:41-47 describes the early Christians assembling together. 1 Corinthians 11:18 speaks of the Corinthian Christians coming together for the purpose of worship.

 4) If people absent themselves from the worship assembly they cannot speak to one another "in psalms and hymns and spiritual songs" as commanded in Ephesians 5:19. Neither can one teach and admonish "one another in psalms and hymns and spiritual songs," Colossians 3:16. 

5) Hebrews 10:25 specifically warns against "forsaking the assembling of ourselves together." There can be but one conclusion and that is that to absent oneself from the worship assembly is to put one’s soul in danger of the judgment.

Is it Biblical to worship on Sunday? If so where can I find the text in the Bible?

Yes, it is commanded of New Testament Christians (Heb. 10:25; I Corinthians 16:2; Acts 20:7). There is the public assembly on the Lord's Day, the first day of the week (corresponding with our Sunday). Of course, a Christian can worship God through prayer, etc. any day of the week, any time (1 Thess. 5:17, James 5:13).