You have a sportsman RS-2 rebranded Beeman..don't know if yours came in with two barrels .177 & .22. More info>https://www.pyramydair.com/product-all-reviews/m/beeman-rs2-dual-caliber-air-rifle-combo/1334
I don't understand why that gun was painted over like that. Just suggestions. When I rebuild and old gun. Get to down to bear wood and refinish with a varnish/poly mix. I'm never trying for fine furniture. I doubt you'll be able to get the original stainless look. Rebluing is to much trouble for me. I just spray paint the exterior metal flat back. A simple slip over rubber recoil pad may siffice for the back end.I wonder when it was painted if both ends of the bore was plugged to prevent paint from getting in the rifling and the crown. I usually slide q-tips in both ends with .117.
I was looking at your picture of the bottom of the receiver. It's been awhile, but the last time I put one of these Chinese Beemans back together I used an extention with my spring compressor an got the spring and spring guide past the long narrow slot for the cocking linkage to slide in. Stuck a screw driver in there to hold the spring and guide out of the way. Then I could easilly at my leisure install the trigger and then just snatch the screw driver out.
Try some acetone to the metal, maybe laqure thinner or enamel reducer.
Remembered what I used as an extention for my spring compressor. An extra muzzle break/weight I had laying around.
I've always had plenty of sockets laying around. It's not to hard to find one that fits for an extension.