Lays out what rent is, terms, Security Deposit, also need to get a copy of current lease.Personally, I would have No issues with buying with tenants in place, if everything looks good, Security Deposit, Current on rent, etc.

The $14,000 was that cash required to secure the hard money loan?

And is it ok to keep the security deposit for lost rent?

I suggest you change the locks, give her keys, and have her buy some security cameras that she monitors through her phone.

With the long term tenant of 12 years, the security of the small return is worth the risk of the monthly cashflow.

How does it work with securing a mortgage loan under an LLC?

If you were to go with the HELOC option, at best you would be able to secure a line that brings your Loan to Value (LTV) to 85% though its typically closer to 70-75% depending on your lender.

Hope that this helps and definitely wishing you and your dad the best of luck in securing his dream home.

If it's not yet on market, see if you can explore some creative financing with the Seller that could include a Seller financing option or an extended escrow that gives you the time to secure the funds to purchase. 

Try to secure two or three that will answer when you are in the middle of a crazy situation.