I've had mine for about 34 or 35 years now.
If its not a match rifle it won't hurt to remove it from the stock. The match rifles are bedded into the stock and removal/replacement in the stock breaks down the bedding compound and ruins the surface contact area/force with the receiver.
Dry firing shouldn't hurt it. It's never hurt mine. Dry firing has always been a training method (dry firing = pulling the trigger on an empty chamber).
I haven't touched my sights in years. I also don't smack it or drop it or turn it upside down on a table top when cleaning it so the rear sight aperature doesn't contact anything hard.
I over oil everything I have. However, on the M1A there are several points you really should use grease on vs. just oil.
I put grease (I use marine grade bearing grease but other folks juse other types) on the bolt lugs and the reciever rails, on/around/in the bolt roller, in the rail/groove the operating rod tab rides in, on the hammer where the bolt pushes against it when cocking the hammer, on the operating rod guide, on the recoil spring, I even put a small amount of grease on the receiver legs where the trigger guard locks in and a little bit inside the receiver where the back of the bolt slides against it while sliding back into the receiver and cocking the hammer.
Shoot GI surplus ammo in it. The M1A needs a certain pressure at the gas port to operate properly without damaging the operating rod/gas system. If you reload there are several powders that are okay. I use IMR4895. I've used Win 748, IMR3031 and Varget, but settled on IMR4895. There are more that are okay but be sure you pick the right one. Lots of info out on the internet and in reloading manuals about it. Also, stick with bullets under 180 grains, too.
They are great rifles for serious work. Or deer hunting!! I carried several rifles over the years while deer hunting (Rem. 742, Springfield 03A4, sporterized M1917, etc.) but it seemed the M1A was in my hands whenever a buck decided to walk out of the brush/woods for me to take a shot.
Mine was in a wood stock for years. Then I bought GI synthetic stock and put a krylon camo paint job on the rough old GI stock and my rifle's been in that one ever since. The synthetic stocks won't absorb moisture, or dry out, and warp like a wood stock can.
I've used my old GI cleaning rod for years when cleaning my rifle. I sometimes use a civilian rod but not always.
Big thing when cleaning a rifle barrel - DO NOT push the patch or brush through the barrel. The compressive force created by pushing bends the rod so that it rubs the lands of the rifling. PULL the patch/brush from chamber to muzzle. Pulling keeps the rod straight (as long as you go slow and keep it centered in the flash suppressor) and removes the crud from the barrel. Why push the stuff you're trying to clean out of the barrel down into the chamber?? Get it out of the barrel and the rifle and keep the chamber cleaner.
Good luck with it.