Most pumps will have either a filter directly on it, or use a stand-a-lone filter mounted close to it. At 20 years old, though, all bets are off as to what you currently have!
YES! Always flush the fresh water tank a few times a year if not using an additive. Depending on the tank size, a few ounces to maybe a cup's worth of bleach is all you need. Pump the water through the system and let it sit overnight. Then run it dry through all faucets and refill the tank with a few gallons of just water and run dry again. Repeat if needed. If not used regularly, fresh water will not stay fresh. I also use an additive that is designed to help keep the water fresh and I only flush once a year... but probably wouldn't even have to do that. You could also use a capfull of bleach each time you fill up to keep things fresh.