If that were my rifle I'd put a little oil on the bolt and hammer and forget about it. Looks good to me. I'd put a few drops of light oil in the action wipe the whole gun down and then go shoot it.
As for the grouping. At 100 yards my bolt action 30-06 with sporter barrel will shot one hole dead cent with a cold barrel every time. Second through fifth shots 1 to 1 1/2 right, left, high low. By then the barrel is "HOT". It will then shoot a three shot group that touches close to center. Then it opens up again. I don't shoot it until it gets hot anymore. Shoot one put it in the rack for 20 minutes. Then again. It will shoot one hole all day long like that. It's also very picky about ammo. My Marlin 45/70 leaver gun will shoot a 1" to 1 1/2" groups at 100 all day long cold, hot, clean, dirty, whatever. Rifles are strange beasts. But fun!