1. You will be fine as long as those PCs are not toasters, though mind that BF2 is a win32 app and it doesn't have multi core optimization, and bots can be actually resources hungry, but you can setup the server on one of the cores, and run your game on the other. Problems will start with stupid amounts of bots.
2. Bots are absolutely terrible in BF1942/BF2, but some people tend to say, they are actually a little bit smarter in BF2, keep in mind than both FH1 and FH2 don't have bot support on all maps, but they have still much more maps available than vanillas. I'm not much of a SP/COOP fan, so I have no opinion on that.
3. COOP/SP is not super stable in any of those, I can't tell how stable BF1942 is on Win10, but I can assure you that BF2 / FH2 run fine on Win10, but even though FH2 is probably one of the most polished mods you can find, priority number one is multiplayer, and SP / COOP can crash every now and then.
4. N/A
5. Not worth the effort. If you into fancy graphics, just don't play BF1942, FH1, BF2 or FH2. Those are 10+ years old games after all.
6. There is a crazy minimod for FH1 called FHSW which adds a ton of new content, but I think they dropped COOP / SP completely and it's multiplayer only. I dunno what are you looking for in Forgotten Hope, but if you're into WW2 history, FH2 is the best you can get. If you like lots of content and FH1/2 won't meet your requirements, vBF won't either. Gameplay wise BF1942 is very arcade and almost cartoonish to me, BF2 is a bit better, though I definitely prefer FH2 over all (it has bit of learning curve tho). Vanilla stuff will certainlty be far more stable than any mod ever made, no matter the game.
7. Overall, BF1942 and FH1 aged really badly in my opinion, FH2 is far better in terms of graphics (still outdated tho), historical accuracy, content (FH1 had more fronts and armies available, FH2 has more vehicles and weapons, and maps being often 1:1 copies of real places), FH2 is also much easier to install (all you need is
http://playfh2.com/ ) and of course FH2 is still being developed, so you can expect more exciting stuff in future