People have provided you with multiple options.

I havent gotten an insurance for this and a week after close I consulted some insurance provider and he didnt offer me insurance options.

Please correct me if I'm wrong.You can require them to have insurance, but you cannot require them to purchase from a specific policy provider.

Contact the utility provider and get a historical average based on the last year of use.

There are cheaper markets that your current savings would go further and possibly provide better opportunity (almost definitely in the short term).

Homeowner insurance provides coverage for owner-occupied property.

Would it be safe to purchase a new fridge, deduct maybe 1/2 of cost to replace  current fridge door from the security deposit, provide receipt with explanation?

Also, what others have said, the personal touches on what is in your place (e.g. providing all the essentials instead of having people buy TP, coffee, shampoo, etc.) and the quality of those items (no tattered towels, stained sheets, etc.).  

Please provide case law where that has happened.

Who is your favorite DM list provider and why?