Sorry if this is a dumb question, but I am wondering if it is okay to use 12v for HIGH,LOW input signals on the analog side... like for a push button. Can the board handle 12v in or does it have to be 5v?
What would be the best way to go about things if I only have 12v and no voltage regulator handy?
NO! You must limit your inputs to the range 0V - 5V else you may damage the chip.
You can reduce 12V --> 5V using a voltage divider
You could use transistors to solve this.
12V to the Base to switch 5V to input pin. Something like a 2N3906.
Common practice, as well as using optoisolators.
What would be the best way to go about things if I only have 12v and no voltage regulator handy?
Give up and go home and stop destroying perfectly good components.
Alternatively you could use the 5V that comes off the arduino's 5V regulator line when the 12V is connected to Vin.