You have to be careful not to give deposits for funding apporval; that is mostly likely a scam.Reasonable costs for appraisals, property inspections are acceptable.  

If you want the home specifically tested, you should ask to do that. 

Fast forward a few weeks, we found a great duplex that we were able to get our offer accepted on - we're pretty excited!

The # of Realtors in your area is probably high, and although the courses and tests to get started are not that tough ( in Texas), like I said there are plenty of Realtors looking to pick up clients.  

Almost none of them have good credit so they accept they have caused the need for the slightly higher deposit.

Accept responsibility to educate yourself!

We are currently in a dilemma because we just found out we had an offer accepted on a house that we really liked, but earlier that same day we found a house that we LOVE and put an offer in on that one too.

I've found a lot of newer people will be more accepted in the Multi Family world because it's a team sport and if you can bring value to a team who does syndication or a 506(C) or (B) raise you can learn a lot and its quite lucrative. 

Ask these people what is the least they would sell for, would they accept X if you paid cash and closed quickly.

I didn't ask but I'm thinking that they will only accept payment from the owner as well.