I am reviewing my HUD statement and last 9 months taxes, security deposit for both sides, and prorated rent is in 200 section and is being applied to the loan which I am taking.My questions.

I am buying two duplex's which are currently rented, what is the rule or law when dealing with security deposits? 

Your post above simply reinforces again the misleading conversation I had on the phone.What really disturbed me and cemented my decision was the post by @Eric Tinsley on this thread. https://www.biggerpockets.com/forums/92/topics/203379-do-hard-moneyFor ANYONE to take a $2000 deposit (I thought I was told $2500), and then tell the client the property they already submitted doesn't qualify is beyond absurd.

The plan designs itself based on the financial profile of the market(s) you are investing in, matching the financial criteria your "financial goals" dictate.

Another thing you can do is ask for a big non refundable deposit.

If someone accidentally writes a check to you for the business and you sign it over and deposit it in the business would not be an issue.  

This tells you from the outside that there is opportunity to add value in updating the property, but also, the inside may match the outside (original cabinets, pink tile in bathroom etc.)Aside from deferred maintenance, look for properties that are on busy streets, next to a gas station, or has any challenges to them.

Has anyone also done a pet deposit with section 8 and charged additional rent fee per pet (and per month)?

Has anyone also done a pet deposit with section 8 and charged additional rent fee per pet (and per month)?

Rents and security deposits should always and can akways be dealt with outside of closing specifically so they don't mingle with and cloud the 1031 proceeds.