Parker VH 12 ga.

[B. Dudley]

Welcome to the forum and thanks for posting photos of your Parker.
A few other observations on your new gun... The buttstock is not original. It is an aftermarket replacement. Things like the shape of cheeks, grip and comb point to this. As well as checkering. Also, the frame on the gun has been blued. This is an incorrect finish since frame should be case colored. Likely the barrels have been reblued as well if the frame has been. Bluing looks to be done a long time ago since there is some substantial wear to it on the edges from use.

To address some of your questions.
The top levers on Parkers being right, left or centered do not really mean anything. Parkers have a bolting mechanism that changes position very little with wear. Other guns will have levers that move a lot as the gun wears. Namely ones with rotory bolting like fox, LC Smith and NID.
You will notice that on Parker guns the rib is a concave surface. This surface carries back onto the frame and also the top lever. This "dish" as I call it was filed into the frame and lever after the barrels were fitted. So, the top lever was set and then the fish put in. Every gun has its lever in a slightly different position. And the amount of wear that the lever allows is very minimal.
Your "dish seems to be a hair misaligned to the left suggesting possible wear, but this may just be poor polishing of parts when the gun was blued.

The hinge pin slot being out of line is not a major issue other than cosmetic as long as it is tight. Again, it was most likely put out of whack when the frame was blued.

Not sure exactly what issue you are having with the shells, so I cannot advise much on that.