Huge list of repairs?

I am a beginning landlord and my property management company came to me with a huge list of repairs. Some of these repairs seem like they are the tenant's fault. (example: closet door hanging off the hinge, holes in the walls, crack in bathtub)

My property management company wants me to pay the bills for the repairs.

Any advice on how I could get the tenant to pay for some of the damage ?

Can I use my property renter's insurance for any of the big things (example: replacing the flooring)?