Well a couple of things. First of all, PCS is not one of the big four grading services, PCGS
, ANACS, and ICG. All other grading services and that includes PCS are not for the benefit of the owner of a coin but rather for the benefit of sellers of their improperly and over graded coins.
Most PCS holders I've ever seen are just like yours where they don't put an actual numerical grade on the coin but rather a classification, and in that regard they are usually pretty close and within the correct ballpark. So since your holder says Genuine and Un-circulated, it's probably Genuine and Un-circulated, but most likely in the lowest Un-circulated designation. So even though the pictures still aren't that great I assume it is MS-60 to MS-62.
You also asked about value. An 1882 P is considered a common year and mint and has a full retail value in MS-60 to 62 grade of $50 to $60, if it was graded by one of the big four grading services and in one of their holders. But even at that many are sold at $35 to $45. If you were to sell your coin at eBay, you could expect the winning bid to be $25 to $40. It's possible it could go for even less or more, but that is what happens in auctions, you just never know for sure until the final bid.
Well I hope this answered all three of your questions.