Have been careful not to accept any partial rent payment. 

I gave an offer but doubt it will be accepted.

We use the same process locally, unless there's language in a listing about not accepting blind offers.To your specific questions on taking a trip to visit all properties and then decide? 

However, if tenant does not move in for any reason, other than Landlord’s decision not to rent the apartment, this holding fee shall be forever forfeited and shall not be refunded.Landlord Signature DateBy my signature(s) below, I request that the landlord accept $XXX.00 as a holding fee for (Address) and the payment of such fee shall result in the Landlord not accepting any other tenant(s) for rental of this apartment up and until the commencement of my lease on (Lease Start).

Or, should I accept with conditions if one or more applicants do not meet the minimum credit score?

That smacks of distrust or micro-management.I have this discussion with my owners before I accept the job.

Eyes wide open acceptance of the risk is needed. 

The estoppel is a form filled out by the tenant, then confirmed by the Landlord, and then accepted by the Buyer.

Can I ask for credit up to the amount of replacing the hvac system which I doubt the seller will accept or just pull out of the contract?

I wouldn't be super punitive on this since you continued to accept payments monthly until they wanted to pay off.