Re: non-Catholic religions, the Eastern Orthodox also believe in the assumption. They tend to call it the dormition, and they tend to believe she died and was resurrected before being taken into heaven. Catholics are also allowed to believe that, but in the Catholic Church it is also common to believe that she did not die. Either belief is currently permitted as long as we believe she was taken body and soul into heaven.
Re: biblical support, here are a few of the basic passages that support Mary’s assumption:
Revelation 12:1 “And a great sign appeared in heaven, a woman clothed with the sun.” Verse 5: “She brought forth a male child, one who is to rule all the nations with a rod of iron.”
Psalms 45:9-10 “On your right stands the queen in gold of Ophir.” – This Psalm is a prophecy of Jesus according to Hebrews 1:8-9. And it says there will be a woman beside Him who will sit at His right hand.
“The New Eve” The early Christians compared Jesus to Adam and Mary to Eve because Adam and Eve were part of our fall while Jesus and Mary were part of our redemption. They were not subject to death because they were prepared by God to destroy death along with the sin of Adam and Eve which we inherit. Also, Adam and Eve would not have been subject to death if they had not disobeyed God. Jesus and Mary took the place of Adam and Eve in the New Covenant except they obeyed God’s will. They don’t inherit death because death is the result of the original sin.
“The New Ark” The early Christians also compared Mary to the Ark of the Covenant because the Ark of the Covenant carried the presence of God for the Israelites in the Old Testament, and Mary carried Jesus in the New Testament. 1 Kings 8:1-6 explains how the Ark was brought into Solomon’s Temple, and other Scriptures, including 2 Chronicles 6:41-42 and Psalms 132, say that this was a prophetic symbol of something the Messiah would do. Since Mary is the New Ark, this indicates that the Messiah was going to take His Mother into the New Temple – and that Temple is in heaven, Heb. 9:24, Heb. 8:5.