Am I in the right to keep her deposit?

[Emiline Lyell]

Pictures of a few spots but every corner of the house is like this throughout. 1,400 sq ft. 

Paint was a year old in great shape when she moved in and she was here less than a year. Every room has a few pieces of furniture/personal belongings. Every inch is filthy, crayon, stickers and animal feces everywhere. Washer hookups are broken. Also lots of small things filter & smoke detector batteries need changed, hardware is missing from one cabinet. I'm shocked that she is expecting something back. I'm itemizing as required but it's hard to know how much is fair to charge for things when we do a lot of the work ourselves. The "normal wear and tear" thing confuses me too. If it's beyond normal, do I just charge what it costs to fix it or do I have to discount the cost for "normal wear and tear"?

My lease does require and I reminded the tenant that the property needed to be thoroughly cleaned although professional cleaning is not required. Everything else listed above is also required by lease. 

Big ticket item here is the cleaning. What would you itemize for cleaning? We're leaning towards $800. I got that quote for a similar sq ft house although that was a construction clean out so not sure if pricing would be similar. I see most housekeepers charge like $400 for a deep clean in my area but certainly this level of filth would cost more?

Located in Virginia.