Can you claim the BF ? Yes if he files as a dependent (if he files at all) and lived with you ALL year and made less than $4400. But before you determine if it is better for him to be a dependent or not figure your returns both ways and then make a decision.
As for the mortgage interest ... if you are not on the loan or on the deed then you cannot take the interest as a Sch A deduction even if you paid the bill.