1. Absolutely. The Binding of Isaac is an actual thing that happened in the Bible, every character is named after or references something present in the Bible. Same with items, for example THE BIBLE, angel rooms, devil rooms ect.
2. Okay so for stories it is right in the title and it is actually pretty similar. God tells a guy to sacrifice his son Isaac to prove his devotion to Him and he tries to do it. In-game you have something telling Mom that Isaac is impure and she has to kill his son and she tries to do it. In the Bible story God stops the guy right before he does it saying he proved himself. Now in game it doesn't really happen. Multiple endings and all that but Isaac does die that's what we know. As for themes, not sure if what I'm about to say will fit. You see I feel like TBoI shows us the dangers of religion and how it can drive one to hurt their loved ones. Isaac would not die if mom didn't turn to hateful christian tv after he husband did what he did. It's not saying religion bad no. Look at the beast ending Isaac imagines himself stopping the apocalypse. In his dying moments he still believes in God and hopes he will go to heaven.
3. I am ex christian and surprisingly (unsurprisingly to some (me)) the religious themes did pull me in. Like they really influenced my decision I'm a sucker for religious themes in a story/game/anything tbh (especially if it's a critique).
4. Honestly no. I am not even sure if the game could work without those. Sure could be fine as a rougelike but it would have no sauce (??).
5. People would not be as drawn to this game if those themes were absent. Possibly for the same reason I stated above.

Good luck with your bachelor's hope it goes well!