A. How often do you clean the bore on your 22LR
Generally after firing for rifles I want to keep in top condition, or when the chamber starts to get "sticky" as the waxy buildup from the ammunition starts making feeding and extraction problematic.
B. What solution/cleaner do you prefer?
Automatic Transmission Fluid for lead and carbon. A foaming copper remover for copper (not generally an issue with 22 target rifles). Honestly any of the cleaning products on the market work, some work better, some just work different.
C. Any danger using copper brush in the bore?
Not really, as long as it is used appropriately.
D. Is bore snake any good as a quick cleaner
It is better than nothing, but pretty worthless for a target rimfire rifle. You won't fire so many rounds in a match that you'll need any cleaning during the match. I know a High Power shooter (multiple Presidents Hundred qualifications now) who uses a bore snake after every stage of a match. Nothing wet down the bore, but a dry bore snake to pull off the hot carbon from the bore of his Service Rifle.
E. Do you run patches thru the barrel until they come out totally clean or slight dirt ok?
No, not any more. A slight amount of carbon is fine. If you run the patches until they are completely clean, then wait a week, odds are you'll get more carbon off if you try to clean the "clean" bore.
More bores have been ruined from over cleaning than under cleaning. With rimfires it isn't even carbon that is the big problem, it's the grit left over from the priming compound. Older 22 match ammo had a different priming compound, supposedly the change was around 1981 or 82, and the "new" priming compound residue is harsher on the bore. So the life of a 22 rimfire match rifle is about 30,000 rounds now, give or take. If you clean every 500 rounds that's 60 cleaning sessions for the life of the barrel. For 250 rounds per cleaning session that's 120 sessions for the life of the barrel.
Always use a bore guide, consider this the best advice on cleaning anyone will ever give you.
F. Thanks
You are welcome.
Jimro