1) The same JP1 cable and the same learning to use JP1 can then be used on both the 15-2116 and RCU810, so the second one is "free" in both those measures, BUT the RCU810 does not come with JP1 pins soldered in.

An RCU810 is harder to reassemble (after you take it apart to solder in the JP1 pins) than a typical JP1 capable remote, and you need to do a cleaner job of soldering or trimming flush to the opposite side of the PCB than, for example, a URC7800. If you are good at soldering and you disassemble carefully (to see how to reassemble) it won't be too hard.

2) I'm pretty sure a base PS2 does not receive IR. When you buy the remote as an add on, you get the remote and the IR receiver. If you somehow have the IR receiver without having the remote (or if I'm wrong about the base PS2 not receiving IR) then you can take advantage of the fact that others have already posted the IR code details and you can use that to program your JP1 remote without learning from the orriginal.

IIRC, people have posted details of two totally different IR protocols for PS2. I believe this indicates that one of the brands of the IR receiver plus remote sold as a PS2 add on uses a different signalling system than that used by some or all of the other brands. Unless there's a third one out there that no one has posted about yet, the worst that means is that you need to try a second upgrade if the more common one doesn't work.