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.

One common rule of thumb is to take 80% of the purchase price for improvements and 20% for land.Another way to do it is to look at the county's values for both land and improvements and use those to determine the percentage.