I have this hole in my firewall below the gas pedal, probably caused by a rat. What is the best way to patch it up (or the cheapest safe/reasonable way)?

 

One cheap and fast way is, ,,If you have any pull open lids of canned goods, just place some adhesive/caulk around the hole and cover it with the can lid.

It does appear the throttle pedal pivot could use some lubricant before it lets go on you.

The hole appears to have been made by a person , too clean for a rodent. I could be wrong !!

 

It looks like your pedal is too close to the floor. How many inch from the base of the pedal to the floor? Measure the brake pedal too.
Move the gas pedal by hand (lift it up) how much free play do you have?