Yeah, most regulators can handle 100psi without any problems. Check the label on the regulator and make sure though; the maximum inlet pressure will be shown on it. Lowes, Home Depot, and other places like that have them for around $20. They also have moisture traps / filters for about $20 as well.
You'll probably get at least 30 minutes of solid painting at around 15-20 psi before having to recharge your tank. I have a 6 gallon 140 psi compressor and it kicks in about every 10 minutes or so, but that's to keep the tank pressure between 120 and 140 psi. I've never shut it off and painted until it stops, but I'm sure I could get 30 minutes out of it.