Free to tenant and myself.Usually hits the bank account 1-2 business days.

One lender aware of and involved in both escrows would have caught/solved this well in advance of one business day before (not) closing.You might still be able to close on Monday on your deal, if you haven't contaminated the joint account with funds only in her name. 

The last red flag was that the seller wanted me to make my ability to secure a mortgage/insurance/inspection conditional only for 10 days including holidays and weekends which is like 7 business days max.

You have 10 business days, 2 weeks, from the end of the attorney review period.Your agent has to know this, and should have told you, if they were looking out for your interest.

I received an email back with the owner's name and address the next business day! 

It can be as small as the next business day or as large as the day before closing but we try to remain reasonable and not waste people's time.

They should be able to give a response by at least the next business day. 

I knew the area and the potential so we told him for this X price we would take the house as is and close in 10 business days.

In AZ its 10K down upon winning the property then the balance due next business day.

However, after doing some more research with companies similar to these, I am wondering if I should cancel my contract (they have a 3-business-day cancellation/refund policy) and instead set up an LLC with a recommended attorney located in my area.