Answer: Yes & Yes & No.
The Bible is clear that God chooses us. The Bible is also clear that we can reject Him. So what gives? Well,
One cannot reject something until it is offered.
None of us can respond to Him until He chooses us. But after He chooses us, we are all free to trust Him (believe in) or reject Him.
When He chooses us, He offers His Son Jesus' works and life as a substitute for our own. I trusted Him. What about you?