1. They should probably do fine. Make sure you put the server on the one which has the highest single core frequency, as the old engines don't care about number of cores, only speed.
2. I find bots a bit smarter in BF2 but it's not really that noticeable. They still get stuck often and are lousy in following commands.
3. Both FH1 / 2 are quite stable up to Windows 7. On 10 I crash much more often but it might be the fact that I haven't reinstalled Windows in like 4-5 years on my current PC.
4. No idea about this. You probably don't need to install anything extra.
5. I believe there was / is a sound and texture pack for FH1 somewhere (check pixel-fighter.com, the last home of FH1 community). I know there's one for FHSW and it's quite good, but FHSW doesn't have bot support so I'd recommend you bring your kids to the FHSW server on the weekend fight nights - 40 - 60 people gather there at times). For FH2 there's only some sound packs but I think they're all outdated. You can try installing ENB with some presets ... For vBF1942 there's this, if you can get it to work:
https://www.moddb.com/mods/high-definition-remaster6. FHSW has a LOT more content than FH1 if you don't mind secret weapons and historical inaccuracies. It also has quite a few different gameplay mechanics including: angling affects armour penetration, different ammunition types, ability do duck when manning a mounted/stationary MG, working bomber bomb sights, working altitude meters for planes and many more I can't recall right now...
7. FH1 and FH2 are different beasts. The only common thing between them is the love for history. I'd say FH2 is a more polished, aestetically pleasing version of your first high school crush (FH1), you know the one you actually managed to marry and it has been a perfect marriage ever since