I knew they both needed some extensive work and estimated rehabs from the pictures on the MLS.

I don' want to get too creative in this response, but there are many of ways to have your way with sellers to accomplish your profitable deals.Write an offer on a skinny contract with a delayed settlement subject to possession - always use "banking days" and build-in an automatic extension - this way you will have it when you need it, (and you will, nothing goes  as expected!)

Their current lease expires this month and they are anxious to know that they can stay, so I feel like giving them an extension until October is the right thing to do even though a risk for me of having to put it on the market at a bad time of year.

I've poked around the internet extensively looking for a calculator I like but haven't found the perfect one.

Are there any landlords here that have corporate rentals? If so, shat does your criteria look like?

Also have done extensive research. 

Your fiance may be able to negotiate a lease extension with the new buyers.Good Luck  

NIcky Redear is right you probably can't enter into contract until you're 18 unless you're an emancipated minor, but look at the bright sight you have all this time before you turn 18 to do extensive research and safe money for your first great deal.

Extension fees?

One side may be month to month as most lease term revert to month to month unless an extension is signed.