Thank you both for your input, I very greatly value constructive criticism like what you have provided me!
I agree that the character should only face forward or back, I never really payed attention to it while developing. I've never encountered the problem where the player bumps into background objects, since I never put colliders on background objects. If you were thinking the rocks and crates are "background objects," they're not, they were meant as obstacles to get past. I also never noticed the fact that shooting collision fails when standing close to a wall, thank you for the feedback!
Someone did suggest adding in a "peak" mechanic, where you can look into the other timezone to see which obstacles you're about to switch into, and I'm seeing that come up more and more as more people play the game, and I think it would be a good idea. If I continue to develop this project, that will definitely be something I will add in.
As for the gun warm up time, I added that in because if the gun shot automatically, the first shot would fire into the ground due to the animation smoothing between the gun raised and lowered position. It could be solved by either having the gun always in a ready position or shortening the time taken to raise the gun, but I agree that it isn't fun in its current state.