Some breeds are seasonal breeders, and will only have heats starting fall and into early winter, because they want spring kids. While some breeds tend more towards seasonal breeding, individuals will vary a LOT.
How old a doe can be bred depends on her individually. I know many well maintained does who are still breeding at 8. I have one myself that I just bred the other day, who is 8 years old. I've heard of breeding does until 11 or older. It all depends on soundness.
For full size dairy does, the rule is 8 months or 80 lbs. It is generally the rule to wait until 8 months to breed a doe for the first time. Yes, there are younger that have made it through their first kidding alright, but it is risky.
You can keep a BUCK with does all the time, but depending on your herd plans it is usually not recommended. First, you never know when to expect kids. If you have dairy does you don't want them breeding 2x per year, and the buck odor supposedly can cause the milk to taste strong. Also doelings CAN be bred at a very young age (3 months or YOUNGER) so you'd either have to wean at a young age of about 8 weeks and raise doelings separate until 8 months (though most prefer to wean at 12 weeks), or pull all doelings and bottle raise.
Hand breeding is not difficult, especially if you keep your does right next door to your buck so you can see them flirting together, then just throw them together for a few successful breedings, then separate out again. You then have an exact date to expect kids and don't have to worry about the issues with keeping a buck with does 24/7.