Gosh, you certainly have a lot of questions today.
I had the opposite problem by trying to limit the number if respite weeks at a time. OH wasn't self-funding so we had to go by what SS allowed us. I was given three respite weeks a year. It used to go up to eight respite weeks a year, then they became stingy. Anyway, care homes don't like to give respite for just a week at a time, they hate that. Minimum is usually two weeks, in on care home they said three weeks. If you get only three weeks a year, that's very difficult, but what I'm saying is that I don't think care homes will restrict your weeks - on the contrary, they seem to encourage longer time periods, I guess because it's easier if they don't have to admit new people every week.