I'll number my answers to match your questions.
1. If the bore is real bad, or jerky with the push through slugs, run 30 rounds before checking the bore again. Guess from there on how many to run with the next lot, by how much better the PT goes through.
2. Only clean before you run a fresh push through. The compound left behind actually builds up gradually until about the third shot, which makes the lapping go faster with the bore so 'charged'.
3. Use any bore solvent to clean, or paint thinner if you like. A bit of lube, such as gun oil after cleaning with a powerful solvent, like acetone or laquer thinner, will make the push through slide better.