Is there a way of assigning Alt+F4 on my bluetooth keyboard to closing an application?

Is there a way of assigning Alt+F4 on my bluetooth keyboard to closing an application?

every OS has its own shortcut and android doesn't recognize what "alt" means.

That function (Ctrl+F4 also) is baked into Windows. You'd need a key remapper app to have Alt+F4 simulate the back button being pressed.