Meeting them to sign the lease is my only chance to really go over what important to us.

My parents are willing to take a chance on me because they see the passion I have to get started in real estate.

The property manager had someone go out and give an estimate for around 11k to replace the entire roof.

There's a very good chance the issue(s) you face have already been discussed and answered.Ask questions in the appropriate forum.

Truth is, for someone young, and inexperienced going at this for the first time, the chances of you falling into a trap are very high. 

The property will be available to view early next week (after the holiday weekend) for estimates for the job.If you know of any solid, reliable general contractors who work on rental investment properties . . . your recommendation would be greatly appreciated!

However, there's always a chance. 

I have been able to find deals in the current market using the BP calculator that fit my buy box, but when I see that homes in that area are estimated to be ~30% overpriced and am watching in real time prices drop it leaves me unsure what to do.

I want to give them a chance to provide a fair resolution and improve the work before I terminate the contract & fire them.  

Setting aside 25% of your net profit is a reasonable estimate for taxes, but the actual amount depends on your overall tax bracket.