Thanks for the bug report!
1). You shouldn't alt-tab out of the game from full screen, because it will screw up the way that the game draws gfx to the screen, and your desktop will be in super low-res.
Sorry. You can however play from windowed mode and move to another window (which will pause the game).
The window resizing I cannot fix either. This is a bug caused by the GM interpretter.
2). I will address this joypad issue in the next update (Sunday/Monday?). The bug is caused by the dodgy 360 pad support that I shoehorned in last minute. I'll post here when it's fixed (like you say, there should really be a joypad on/off switch, ideally).
At the moment, the game always looks for keyboard and joypad input, so having a non-compatible joypad plugged in will cause this issue (movement requires a POV hat), and I guess that not even joy2key will help.
For now, the only solution will be to remove your pad and play via keys