Do I need them to sign a new lease for June and the rest of the July or will a 39-Day notice be enough since I already have rent payments and the security deposit? 

It's very common for small business owners to understate their expenses and overstate their income.The overstatement usually is in the form of "We don't run everything through the cash register", especially in a cash business. 

(Multi-fam obviously have some common area exemptions to this). 

. - Most common is to buy the rate down.

We had to decline due to my husband’s medical status, the short notice and the cost of the move (no concessions were offered).

The same common sense rules apply to most things on your credit report - maxed out revolving credit cards and late payments hurt your score, while responsible use of debt and on time payments increase your score. 

Recently in doing some research, I noticed that the property taxes are not being paid. 

In our state, an evicted tenant, or one that has abandoned the habitat has 30 days to remove their personal property.There are also usually  caveats in the L/T laws that allow you to post a x-day notice of Abandoned Property. 

If they are staying and your current lease ended - then they automatically go on month to month and you can only increase the rent by 1.8% and you have to give them 90 days notice of that rent increase as well from the end of their term.  

For off-market commercial deals, it's very common for there not to be a buyer broker involved, and if there is one involved, it's common for the buyer to be paying for it out-of-pocket.After the CRE broker gets the listing agreement, they will shop it directly to their exclusive list of investors.