If this is the case, then do an inspection to verify it is vacant and in good condition prior to any money changing hands.Make sure the security deposits and prorated rents are transferred to you.

Think of all the things that could go wrong and see if the lease addresses them: unauthorized pets or tenants, early termination, security deposit, lease violations, late rent, eviction, lawn maintenance, parking, etc.5.

I have an appt this week to set up the bank account for the security deposits and the monthly rents. 

You aren't allowed to secure the house during the closing period.

If they don’t respond or react quick enough in this market, how do I know that they can secure what I want when time is of the essence?

Upon final walk through found out 1 tenant was applying for rental assistance, this tenant never had a security deposit but the question is not about that tenant.The other tenant supposedly had a $1,000 security deposit.

Also, what did the seller do with the security?

If it's to acquire multiple doors, I would put 20% down (to secure best terms) and invest in additional properties. 

A heads up - before you send out your deposit accounting read the CA laws very carefully -  thankfully laws are changing to protect tenants from over charges from the security deposit - but this means there are very strict laws regarding this. 

I thought the seller was originally going to carry for at least 6 months, but I misunderstood.Instead, I need to either secure bridge funding for 3-6 months or find long-term financing.