Off center pin strikes are common with many rifles, not an big deal as long as they aren't extreme to the point of misfiring.
With an unfired round chambered, place a straight edge across chamber face and the cartridge headstamp, is the case flush with the chamber mouth or recessed? Any recessed amount, plus the barrel to frame gap = headspace, the SAAMI max acceptable headspace is .006", if it's more than that, it needs to go back to H&R for a new barrel.
Ideally, the case should be flush or maybe .001" above the chamber face, even then you'll get some case growth with max and/or some factory loads and they'll need to be full length resized.
Tim