Yes, scuba cylinders can be cleaned and they are if they are going to be used with oxygen enriched air (i.e. nitrox). There is a debate whether they need to be cleaned if used for "low" oxygen nitrox if the nitrox is premixed.

Nitrox is just oxygen enriched air.

If you used pure oxygen, it would be toxic past a depth of 20 feet / 6 meters.

The gas that you can use is filtered air or nitrox, which is nitrogen enriched air. There is CO2 used for some BC vests also for an emergency, you can detonate the CO2 to get up to the surface.

It depends on how deep the diver goes, and what air blend the diver is breathing.

There are dive tables that state how long a diver can stay at a certain depth before requiring decompression.

The basic recreational diver typically breathes either air or Nitrox. There are separate dives tables for air and Nitrox.

Depends on the area - in the Florida Keys/anywhere exotic, expect $10-$15 for air and $15-up for Nitrox. In Daytona Beach, which is the cheapest I have seen, it's $5 for air and $7 for Nitrox. Most major cities are around $10 for air and $15 for Nitrox.