Finance contingency if you need it, should also have an option to extend. 

I guess it can be consider contingency funds?

Should I include a contingency that says current tenants must sign a lease with me at or before closing, or is this going to kill the offer? 

I would definitely add a 15% contingency to the rehab budget.  

BiggerPockets also has a "Tools" tab above, hover your cursor over it and click "FilePlace"... here they have templates and documents that you might be able to search through and find what you're looking for.Once you have the LOI (otherwise known as an offer binder, offer sheet, deal sheet, etc), all you have to do is outline the terms of your offer: Proposed purchase price; deposit amount; total down payment; method of payment (cash, mortgage); contingencies (inspection, appraisal, etc); proposed contract date; proposed closing date and anything else outlined on the form or anything else you'd like to include. 

Just put in a contingency for an acceptable appraisal.If your concern is whether it ia good deal put a contingency in for a due dillegence period and ask for all appropriate documents to verify income and expenses.

You can submit an offer with a contingency that the owner pay for all (or even half) of a foundation inspection.

.- If you are financing, say NO FINANCING contingency. 

We still don’t know what your contract says....is it Contingent on clear title...yes or no.

In CA the only way to get some seller interested in your offer is no contingency, and often no loan meaning if you do not move forward after acceptance the seller can keep your deposit.