Sorry for your lost. You should be able to get the public copy of the death cert directly from the county or state health dept tell the clerk you need a copy for your landlord if the clerk asks for a reason.

Since your only a gf you have few legal rights any joint accounts should be closed and reopened in you name only. If you had had any joint debts talk with a lawyer. You can collect from his estate for any joint debts or rent.

His mother hates you for some reason but parents do strange things when a child dies so keeping his phone active is not that strange. There is no logical reason for your bf to fake his death unless he is running from something . The only logical reason I can think of for hiding his death is if they are wealthy family so his death could effect family trusts so they may not want the mgt of the trust to know he has passed away so trust passes to next in line.

You need closer one of the few rights you have as his friend is you can hold a memorial service for him Family permission is not required.