Dude, I'm pretty surprised you actually want to know the answers to all this stuff. I'll definitely help cover it with you. I'm bad at the formatting stuff like you have, so I'll just try to follow the order you used.
Yes, God created everyone with a different mind and brain. He gave everyone free will. God filled the toolbox for every man and woman, but it is on us to open it up and decide whether we buy what he is telling us. So you want evidence. What does it look like? We know God is not tested for with scientific means. You do not test for non-scientific phenomena with scientific tools. The first, and most basic steps, are you have to see about it yourself. You want evidence, all you need to do is look. Sincerely open your mind when you lay your head on the pillow, and indulge what you find so absurd for 30 seconds. Maybe it will surprise you. Get a book that explains what Jesus really said, and what his gospel is; mean old ladies and TV preachers with big hair are generally a bad mouthpiece for what God is really trying to get across, but they do tend to be the loudest. Go listen in the still of the forest, and look around at massively tall trees and wide open landscapes, and see if that looks a little bit like God's handiwork when you open your mind to the possibility. You asked for evidence, and I'm just trying to bounce some ideas around of what in the world that might actually look like for you. What it won't look like: proofs on the internet, logical flows about disproving impossibilities, etc.
To your second paragraph, you get hell forever if you pick it. Nobody should be surprised where things are sitting, if in fact God is who he says he is. So here is the key thing about sin, punishment, hell, and the rest. God is perfect, and his holy nature means he will and must punish sin. He has promised as much. So what about really good people? My mom is the nicest lady ever. Gandhi helped so many people. Unfortunately, unless you're perfect, you're as good as gone. God is perfect, and he can not abide sin in his presence. That's why Jesus was so absolutely necessary. He came and lived a perfect life, and died as a perfect sacrifice, so that he could take the punishment for us. He offers every single person the chance to trade their F- for his A+, and all you have to do is believe that he is who he says he is. The crack dealer who hits rock bottom and recovers and finds God? White as snow- God doesn't look at his record, he looks at Jesus' record. Gandhi, who was this amazing, great humanitarian? I guess I don't know what was in his heart, but it would appear that he did not accept Christ as his savior, and so he is in a bad way. He keeps his F-, or maybe he got a C-. But it's not the perfect A+, so it doesn't get you in God's presence in heaven. And to your last sentence, God does not punish you for doubt. Even the strongest believer will sometimes struggle with doubt. But if you have that heart change and accept Christ, you will struggle through and work past that doubt, and should always know that he has you securely held.
Bummed, yes, you're right, is an understatement. I mean, my heart breaks about it. I have family who don't know God. People I love, close friends, tons of people. Even you, a guy on the internet. I have tears in my eyes typing right now, that I so sorely wish this would make sense in a way that affects you, that it could somehow bring you closer to understanding and wanting to know God. Christians who do not feel that way are lukewarm, and suffice it to say that Jesus has bad things to say for Christians that are lukewarm.
Christianity vs. other religions is a great question. I don't believe the other religions answer the questions of life how Christianity does. The deep things, like "Why are we here?" "What is the purpose of life?" "Who is God?" "How do I relate to God?" The narrative is completely internally consistent, the story is fascinating and beautiful, and when I look at the whole thing, it clicks and resounds like a math proof or a melody.
I think I covered those questions at the end in discussing above. God's holiness, sin and punishment, God reconciling his people back to him through Christ. Let me know if there's something you want clarified still. I'm glad you asked!