But, doesn't the Bible teach salvation by faith? If ALL are predestined, where is the need for faith?

First, salvation by faith may, or may NOT be correct. It depends on WHO'S faith you are claiming. If you are suggesting that I can be saved by MY faith, this is completely incorrect. Salvation by MY faith is a counterfeit salvation by works. I can do nothing.

Galatians 2:20
I am crucified with the Messiah: nevertheless I live; yet not I, but the Messiah liveth in me: and the life which I now live in the flesh I live by the faith of the Son of Yahweh, who loved me, and gave himself for me.

Its NOT my will, its the will of the Father, its not my faith, its the faith of the Son. What part do I play? NONE! I can't even reject the Messiah Yahushua's atonement, it was already made for me (because I was lost). I can't reject Yahweh's Love (including Grace and Mercy), because it overwhelms me. I can't reject Yahweh's Will, because it overpowers me. If not in this age, in one of the ages to come.

If I DO anything (including my faith or my belief or my acceptance or my decision), I have room to boast of "works". "MY decision" becomes a work of "my faith"; something for which I can boast. Boasts such as "I am not like the majority who refuse to accept Yahweh's gifts and refuse to believe in Jesus." "I am glad that I'm not like the publican."

Paul says that there is no boasting in faith:

Romans 3:27
Where is boasting then? It is excluded. By what law? of works? Nay: but by the law of faith.

We are saved by "grace" through "faith" - but not our own... We have no reason to boast.

Ephesians 2:8-9
For by grace are ye saved through faith; and that not of yourselves: it is the gift of Yahweh: Not of works, lest any man should boast.

So, YES, Yahweh's chosen people will go to heaven if they have been elected and given the gift of Yahweh's grace and faith. But not by any works of their own.