I carried an M14 for almost 3 years. I bought mine in 1978 and have shot it and hunted with it till about 5 years ago when I got an old SA M1 Garand that just shoots rings around the M1A and as well, or better than my old 03A4.
Anyway, back to the questions.
1) for the most part I use a GI cleaning kit. Always have. Use it right and its no issue.
2) for lube, we used LSA in the Army and I used 3n1 oil for years before getting the Garands and going to grease for them. Then I started using grease for the M1A, too. Marine grade bearing grease for increased resistance to water/moisture.
3) A GI canvass sling.
4) as many magazines as I could get my hands on many years ago, before the copy cat/fake GI magazine thing started
5) A GI synthetic stock, so I don't have to worry about the effects of moisture on the wood stock or POI movement due to the wood warping/swelling
I've only cleaned my gas system with brushes one time, about 8 years ago, before I went to a week long, 200 round per day training event. Prior to that I just used powder solvent and patches to clean the inside of the piston, the inside of the plug and the cylinder itself.
I don't even clean the chamber except for once in awhile (I mean with the GI chamber cleaning brush). I clean from the receiver to the muzzle so 1) all the crud goes out the muzzle instead of being pushed back into the chamber and receiver, and 2) the cleaning rod is under tension (not compression) and stays straight in the bore and doesn't rub the lands with the same force as if I was pushing the patch/brush through the barrel. I don't use jags for that reason, they have to be pushed through the barrel.
If you want spare parts be aware that a good number of M1 Garand parts fit/work on your M1A. The whole rear sight mechanism, the hammer, the hammer pin, the trigger, the trigger pin, the hammer spring and the sleeve (can't remember the name of it) and piece that is inside the spring and pushes on the hammer (can't remember the name of that one either). Can't remember if the safety is the same or not. Oh, the extractor from the M1A will work, too, but you may need to grind a little off the bottom tip of it if you want to shoot blanks in the rifle (at least that's what I hear.) The extractor spring and detent should also work.
The M1 Garand ejector/spring and firing pin are different and will not work on the M1A.
They can be great rifles. Like I said, earlier. I'd still be shooting mine if it wasn't for that darn M1 Garand that people think is a match rifle when they see the groups it shoots.