The only issue I'm having is exiting a game once in it.
That's mapped in the emulator. What emulator are you trying to exit?
The first dumb question (and I did read the FAQ) is how do I get the options window back open?
While in Mala, right click with mouse.
I'm assuming this is a MAME keyboard map and not Mala, but if it is Mala, what do I need to do to map the ESC button so I don't have to use the keyboard? If it is in MAME, same question applies
Press TAB while in MAME to access the menu to remap buttons.
What interface is your controller using? If it's a keyboard encoder, you may need to disable multiple keyboards in mame.ini
If it's enabled, it treats each keyboard as an individual device and will only accept input from the specific keyboard that has been mapped (keyboard 1, keyboard 2, etc) If disabled, the same key from any of keyboards should work.