And unless you have previous construction experience, I would stay away from getting involved in a major rehab project on your first rental.A huge rehab (for your first project) could mean you end up with a partially torn apart duplex with no tenants and not enough cash to finish the project literally forcing you into a distressed sale or worse.IMO its more important to learn the process of being a landlord and be fairly safe by buying a rent ready house than it is to make a huge return on your first property. 

PMI has become a dirty word, like ARMs for all the wrong reason.

Hopefully he doesn't force an eviction by staying.

The downstairs tenants were forced to move out which wasn't an issue because they were a young family buying a home so the timing was perfect. 

You could offer to sell back for 12K but you will never see the money, you could raise the rent to $400 but they will default and you will be forced to evict, you could fix and rent for $400 but probably not have any positive cash flow and end up with tenant issues or you could just sell it as is for 12K on the open market.

Also note that once you purchase flood insurance there is a 30day waiting period before the policy becomes active and in force to keep people from buying insurance the day before the storm of the century.  

But I like the BRRR strategy and I'm thinking to start with a multi-family, force appreciate and rent out.

Not having her on the lease is a mistake because when they break up she will stay in the unit anyway because her credit will not afford her the luxury of finding another landlord that will rent to her.You will be forced to go through the process of evicting.

Second, in California, an HOA has to pay the attorney fees for the HOA member, if the member is forced to make the HOA follow the CC&Rs.

Flipper pays for rehab so that puts him at $70kAfter rehab the house appraises for $110k so with his $70k and my $10k that we have into the house there is $30k of forced appreciation that we would split 50/50.