Couple of beginner questions

Got an old 700 BDL in .308 from either '77 or '94 (their serial stamping method seems a bit questionable ), with a 1-piece Weaver base, Weaver rings, and a Tasco 6-24 target scope (I know, I know). I went out and put about 20 rounds downrange today and have some questions.

The big thumb stud screws holding the rings on to the base backed off and I didn't notice, leading to pretty poor accuracy. I obviously tightened them back up, but should this screw be Loc-tite'd? I put some on the screws that hold the base to the receiver, but wasn't sure if it should be done in that spot as well.

For the first few rounds it shot well, but afterwards it wasn't ejecting as well. The handle would rotate correctly up until it had about 1/3 of an inch left til it was fully up and ready to pull back, and it would get pretty hard to push up the rest of the way. Is this normal, or should I look into something? The ammunition was actually labeled 7.62x51 and not .308, and I've heard that though they are safely interchangeable they are not identical rounds, so could this be part of the problem?

Before shooting I ran some Remington solvent cleaner through it on a brush a couple of times, then patched til clean, ran some Kleenbore 3 through on a mop, patched clean, and put a light coat of normal gun oil on the bolt surfaces. Good cleaning procedure? I'm used to shotguns which you can basically not really clean at all, but rifles especially in this larger caliber makes me think I should be a bit more diligent about it.

I think thats it for now, obviously a nicer scope is in order but I shoot roughly once a month at an indoor 100yd so I'm not going to break the bank just yet, I'll probably set the knobs back to factory center and rezero it again but thats about it.

Any other suggestions? Clever methods that you can't read in a book or online? I'm pretty green in the bolt gun topics, anything helps at this point.