question about liability policy, Thanks!?

I recently got rear-ended by a lady in a STOP Light, it was not her fault. There is an Un-insured driver who hit her, and then she bump into my car and took out my bumper. And the one who hit her turned around and drove away. yes, we got his liscense plate number, the Cops pulled out all his info and looking for him. My question is, Assuming the hit and run driver is un-insured, is her insurance company suppose to pay me for the repair even tho is not her fault?

if not, here is my question, Liability insurance is suppose to protect other people's property or bodily injured for the damage you've cause, from what I understand. Let say if an uninsured driver hit her car, and then she lost control and slam into my property, such as my house, and damage is less than my dedectible. even tho is not her fault, and the one who hit her has no insurance, am I pretty much screwed?

I just want some advice before I deal with the Insurance company, we all know they will come up with all type of excuse when it comes to claims.

My insurance company told me they'll look into it and see what'll happen, at this moment, they are still trying to collect information.

Just extra info, I have full Coverage with State Farm, and $500 deductible. However, the price on a New Painted bumper probably runs around $500-800 in my area.