Not-So-TurnKey investment? Looking for advice

[Latimer Luis]

This is my first post, so first of all, "hello" to everyone and thanks for giving me enough courage to jump right into Real Estate Investing!

I'm in contract to buy a property in Alabama from a fellow BP member. He/she may be reading this and I think that's fine. :) The home was just rented out today, but there were some minor issues found after the inspection earlier in the week. I asked that they take care of most of these items, which the team agreed to, but with there now being a tenant renting out the property (this wasn't the case at the time of the inspection), my guess is that it's going to take some time for these things to be addressed. I do have an inspection contingency and I want to make a decision by the morning. 

I asked a few questions and received the responses below:

Should I be worried? Is it wise that I proceed without an addendum or will an E-Mail chain hold up should the repairs not be completed? Would you continue to press for the re-inspection? The team seems reputable, but it's also my first investment property and I don't want to get burned. 

Lastly, with respect to the new tenants, what am I allowed to ask about and what SHOULD I ask for? 

Thanks in advance!