Both games are fixed at 1024 x 768, which was pretty standard when the engine was made. (Changing the games' resolution would involve massive amounts of programming, so we'd only fix that if we did new versions one day.)
Neither game supports Win7-64bit, but we know of people who can play it, and have received just one or two reports of problems. Thus while we can't guarantee the games will work, there is good reason to expect them to.
FOF has no significant problems, and works just fine. COG:EE does have some problems that can affect certain games (mainly PBEM, if I remember correctly; feel free to post a question over there).
As for your last two questions, the battles are only within the broader strategic game, and there are no historical battles (though see the "Brother Against Brother" forum for news of a game we're currently working on). And yes, you build units that are generic, but do have some "Legendary Units" (e.g., Stonewall Brigade) that sometimes appear at their historical time as a bonus instead.
Please let us know if you have other questions!
Michael Jordan plays ball. Charles Manson kills people. I torment eager potential customers by not sharing screenshots of "Brother Against Brother." Everyone has a talent.