It does mean that God chooses from the beginning to pass over some people, yes. It's not so much that He actively damns anyone, it is that He leaves some people to the fate which they deserve. This is the essence of double predestination. See Dr. Eckleburg's excellent link in post #30, which holds that Martin Luther held this very view.
That people who are among the "elect" can do what they please as they are the chosen?
Well of course not. We are no longer slaves to sin, but slaves to righteousness:
Romans 6:1-2 "1 What shall we say, then? Shall we go on sinning so that grace may increase? 2 By no means! We died to sin; how can we live in it any longer?"
That the people who are among "the elect" can then become say Muslimes and they are still among the "elect"?
Such activity would naturally be considered very sinful. It would lead me to wonder to myself if the original salvation was genuine. Obviously, only God can know. However, I can see a member of the elect, especially in the infancy of sanctification, falling into a cult through coercion. We know that spiritual warfare is absolutely waged against the elect by satan, and unfortunate things can happen. Salvation, however, is not lost.
That there is no need to spread God's word as, if there are the "elect", they will come to Christ without the members of The Church helping out?
There is an absolute need to spread God's word, not because it accomplishes salvation, but because it is in obedience to God. Our witnessing converts no one and saves no one. That is completely God's purview. Even though we stumble, the truly regenerated heart seeks to obey God, and for his purposes, he wishes us to evangelize.