Depending on the type of filter you use honestly depends on how often you change it. Disposable filters ( i.e. the cheap $2 filters) must be changed once a month. Pleated filters ( i.e. look like a ruffles potato chip) are supposed to be 90 day filters. They should be checked every 30 days. Things in your home's air change daily. So check every 30, change as needed.
With all the choices out there I know it's hard. If you don't have severe allergies then the cheaper of the pleated filters ( MERV 8) will work just fine for you. For those with allergies, use the MERV rating on the filter to choose the proper filter for you. The higher the MERV rating the more allergens it will stop.
Every 6 months, or before each cooling and heating season. Cleaning your unit extends the life of the unit. It also keeps it working at peak efficiency and your energy bills lower.
Unless you purchased an extended warranty with a new system, and your system is more than 5 years old the answer is probably not. Newer systems ( i.e. 2012 or newer) have longer manufacturers warranties.