(Not a Teacher)
1) It sounds fine to me. I don't think I could quote a rule to you, I'm afraid. We do use that construction a fair bit:
"Timmy is at summer camp for the next two months."
"John has been at boot camp for nearly three months."
"Sarah is at school right now."
"Larry is at home watching TV."
N.B. -- You could use "the" and it wouldn't sound too off, though.
2) I'd use present perfect as well.