If you desire you could rent it M2M with a two month notice required by either party to terminate.

I have some options with business lines of credit as well, but before doing this I wanted to check on why more traditional loans are being discouraged in this case (and if this is common).

This should be a very common policy down there and shouldn't raise your premiums much, if at all.If he is sharing the profits with you it could be a great way to boost revenue, you just need to be aware of your increased liability. 

Send a notice to all tenants informing them that they will each be held responsible for the trash fines.

Yep, I'd provide proper notice to terminate for sure.

While I am new and probably not the best person to offer proper real estate investing advice at this point, I can tell you that one of the common themes I hear from talking to many successful investors echoes what @Jay Helms said above.

Now we need to give her rent increase notice, can we increase her rent based on $650?

He tells me this is a common "takedown" for this type of sale.  

Would you give her a 5-day notice for breaking the lease? 

This is a very common and popular way to get started investing and it's highly encouraged.It's known as "house hacking" around here on the forums.