Hopefully you have a "contract to hold" that stipulates the binder payment is NON-REFUNDABLE (and never call it a deposit). 

If not, have you considered the stipulations of an FHA loan?

Question:  In our shoes.  1) Would people advise firing the PM (we have to do so 30-days before March 5th).  2) Do we have the Tenants (who we will keep, but with a lot of stipulations) fill out new application and run a background check?

Typically note don't stipulate note holder health. 

See lines 268-276 on page 7 of the state contract:"DEFAULT OF AGREEMENT BY BUYER: In the event of any default of this Agreement by the BUYER, the SELLER shall have at the SELLER’S option the right to declare this Agreement null and void with no further demand, or to demand and sue for any of the following: 1) Termination of this Agreement; 2) Specific performance; 3) Termination of this Agreement and an amount equal to 10% of the Sale Price as stipulated damages.

Would I need to refinance their loan and put in new mortgage stipulations ? 

Take a security deposit and treat it like a normal rental.Ensure wording is included that would include clear stipulations on what will happen when things close or if for whatever reason the deal falls through.

I've never seen a stipulation like that.

What are the Capital gains stipulation.

There's also a stipulation that says their rent actually increases by $100 w/ a mth-to-mth tenancy...After some more thought, I've decided to give the tenant a 60-day notice for non-renewal.On your point about inspection: I was planning to do a final walk-thru after she'd left...