I'm no vet, but everything I've read said that heat cycles can last up to 21 days in total. If I were you, I'd call your vet to confirm. Also, a bitch in heat can be bred more than once, with more than one male, and you can end up with one litter mixed with two different fathers if the males have had a chance at her in the same cycle.
Yes, dogs can be spayed while in heat (although they will usually want to watch them a bit more in observation due to bleeding risks - it's a slightly riskier surgery.) They can be spayed while pregnant as well, and the puppies can be aborted (which I recommend if indeed your male did get to your female.) These procedures are usually more expensive (but that's no excuse not to do it immediately.) It's the responsible thing to do as an owner.
Seriously, you're lucky she just came into heat now at a year, as a lot of dogs would have come into season earlier. I would get both dogs into your vet asap, as "mistakes" like a litter of puppies are completely avoidable if handled properly.