As far as locating the corners, if you can't find the corners on the GPAA site or book, the only thing you can do is get the surey from the county. Each county is different.
-In Yavapai county, you can search a township, range, and section for mining claims, and then easily find the survey and download it.
-In Maricopa county its a lot harder. You have to search the entire county for mining claims, manual look through hundreds or thousands of them until you find the name. If you go to mylandmatters.org, you can find who the claim onwer is, and then search for Maricopa county records by last name for mining claims, and then download the correct one.
After that I go to a map like is on mylandmatter.org, or the BLM LR2000 site, and drop a pin on that cornmer to get a GPS. Unless the person has misfiled the claim, which happens, then that takes me to where I can see a corner marker. There's something like 8 X 8 or 64 standard places a corner marker can go, but they don't have to, for example claiming nect to private property, claiming next to patented land, claiming next to an add shaped lode claim. Land Matters and the BLM data will tell you a claim is in the section, but does not give you where in that one mile quare area its located. There's other ways to get Lat Long for a corner of a PLSS survey including county maps, GPS downloadable overlays, or even plotting them off a paper map (not fun).
At least locally, a location monument isn't really used, it s but they build the monumnet on the corner of the claim.
Also, a 20 acre claim is usually to the dimensions you mentioned, but there's plenty of 40 acre 1320 X 1320 claims, and then 2640 X 2640 160 acre claims, plus a few odd L shaped or other rectabgular claims. A few people have done other size claims.