[Radioroslyn]

Hi John and welcome to the Phorum,

#1 I like 22g stranded. I saw this https://www.tubesandmore.com/products/wi...-foot-roll but it seems a bit pricey if you are going to use several colors. I would shop around a bit and see what turns up. Radiodaze sold wire that was in smaller lengths and seemed to be a better price. They have stop selling a lot of electrical products in favor of graphics.
#2 Would use 18g (green) for the 6v heaters and black for the 120v primary. You want to be sure that insulation is rated high enough for the high voltage winding (abt 600v). Philco doesn't use the standard RMA code code for the wiring so it makes it a little confusing for us old timers. The hv winding is fine with 22g.
As for the replacement wiring pop the cover off and put the screws back in the core. Tighten them mark the wires as to which ones are which. Cut the wires reasonably short and use shrink tubing to insulate. Some transformers have a cardboard insert inside. This acts as an insulator also. If it doesn't have one I would consider adding a little something. RMA code would be black for the primary,green for the 6.3v heater, red for the high voltage winding, red/yellow for the center tap.
#3 https://www.tubesandmore.com/products/po...pst-switch Pick 500K. Will have to cut and file a flat on shaft.
#4 I don't think 12mf is a standard value anymore. 20mf at 450v is fine get two. 40 is a bit excessive.
#12 I've used Qtips and a bit of mek (lacquer thinner) to clean the contacts. The washer is there to prevent microphonics (vibration).
#13 Remove rivet by drilling or grinding. Fashion a suitable bracket and use screws to mount it.
#14 With the pointer removed fasten a thin piece of clear plastic over the dial using the two mounting screw. This can be form an used blister pack something from the bakery perhaps. Put a hole in the center for pointer.

Back in the 80's I had the chairside version the 39-7CS. Same as your set but used an 8" spkr. Great player.
GL with your new project!