Hey, thanks for letting us know that you can do gamepad for move (they are activating axis so should indeed work). The turning does require mouse, as I implemented raycast.
Cancel (back) is indeed going to main menu. These things will be changed in the future.
We didn't implement gamepad (aka new input system) yet, two weeks was too short to also focus on that ;)
The shooting through walls has to do with the buildup of the level. The actual build would have solid constructs :D. But in 0.4 I will make sure that all walls block the bullet (meaning you can use ricochet bullets.