this is the official IRS form to determine support
https://apps.irs.gov/app/vita/content/globalmedia/teacher/worksheet_for_determining_support_4012.pdf
suggest filling it out and see what happens. Suggest estimating the expenses that reflect the situation you are walking into.
on the rent question, I wouldn't worry about your boyfriend having to declare the rent as income. This is no different that two non-married people who room together in an apartment or house. when two people share an apartment or house, no one is declaring rent income when only one name is on the lease or deed.
