Stolen Security Back Door- Should I ask Insurance to cover?

[Thu Dinh]

I am experiencing the colorful rainbow of being a new landlord. Please send help... I mean I would really appreciate your thoughts!
I just took over a turnkey from Rooftop with tenants in place. Life was good. Until...Tenant terminated lease right after my purchase. I almost had to convict her on Thanksgiving week (thank God, although she paid 2 months late, she moved out, and I didn't have to be the mean guy). I just finished renovating the house for the next tenants. Listing was up not even a week, the back security door was stolen (Why???) I had the police report and need to fix this, which will prolong the showing. I don't know how much longer. In such a short time, I think I have encountered most nightmares of a remote landlord. 

 My questions:

1. Should I claim/ask the insurance (Real Protect) to pay for this door? Will my insurance increase?

2. My PM said the rent Roofstock had before I purchased was higher in the area $800. How long should I keep this listed before I lower it down?  $750. $650.

Thank you guys!