I purchased a Ruger American and had a Vortex LPVO mounted to it. This is my first firearm I'm not running iron sights on, so there's a bit of a learning curve. I had started to install the scope myself, but decided to let a local sporting goods store finish it because I packed the proper leveling equipment and can only boresight at distances appropriate for pistol sight installs. It was installed and seemed ready to go, so I ran off to the range yesterday to see how close it was. Shooting at 50 yards from a seated position (no bipod or rest) I was unable to get rounds on paper. My initial thought was that the scope had been knocked about too hard and was now aligned poorly (my case is a bit small, I need a better one). After I gave up for the afternoon (50 rounds in, probably should have quite after 10 or 20) I discovered that the rings weren't securely fastened to the rail. There is a substantial amount of forward-backward play, so the scope was never pointed at exactly the same spot twice.

I'm new to this, so here are my questions.

I'm running a 1-4x LPVO (no places for longer shots here, so there's no need for higher magnification), should I be expecting to be able to boresight it and then dial it in on paper (from a rest)?

Can I just torque the entire ring and scope assembly down to the rail, or does all of the work have to be redone? The rings are securely mounted to the scope, but not to the rail.

Can I bore sight at a much closer distance and just do the math based on where the round should hit further out? For example, set it close based on 10 yards and then confirm at 25, then 50, then 100?