Dan, here's my assessment.
1. see
www.bluebookinc.com for the Parker ID and SN book. Price $35. Since your gun SN is not there and you are only interested in learning about your gun, don't buy the book.
2. A research letter is available, but unlikely to show anything more than original shipment to a distributor. Its a base grade gun and unlikely to show anything more, but it's something I would do because I have $40 to spend and I like to know the history.
3. Your gun was a very common form of Parker, a GH, over 18,000 were made. Its highly likely to be in original configuration. I can't tell more without photos.
4. Your major issue is what cartridge this gun is made for. For that you need to take chamber and barrel inside diameter measurements and post them here. Or you can put 12, 16 and 20 ga shells in and see what fits. If none do, then you fall back on ID measurements and you need to post them here.
5. Shooting. You need to know whether the barrels have been bored out and are not original ID. If so, you need to find out wall thickness. If you have original wall thickness, often around .035 in Parkers, and there are no barrel dents, bulges, cracks, rust under the ribs, etc, then Parker original service psi limits apply, which went up to around 10,000 in a 12, but since I don't know what ga you have, I don't know what service limits apply. Its always a good idea to usually use loads less than service limit in any gun, damascus or fluid, modern or old, and many people here load their own or buy shells from RST.