Seems like you should not have to but showing they broke house rules leading to damage may help. 

An attorney is not needed provided your not making a claim of fraud or misconduct/damages are being sought. 

• How do leases typically handle furniture/appliance damage or wear?

Poor communicators, poor housekeeping skills, prescription med abuse, big dogs that they couldn't properly care for, damaging, etc.

Normally, we would say no and wait until the end of the lease but due to the situation and hardships we would inspect for pets and pet damages.

Like deferred maintenance, (bad roof, worn out water heater/AC Unit, warped flooring, water damage) etc, unpaid utilities,  unpaid taxes, a second loan, unpaid HOA fees, a bad pool, bad reputation, sometimes squatters, sometimes they were drug houses, and so on.

Does anyone have a template or method that they use in order to screen tenants effectively in order to reduce the risk of non payment and damage to the property? 

When the tenant moves out and the funds are distributed either to the tenant or the landlord for damages, then the subaccount for that specific tenant has a zero balance and that subaccount is closed. 

Properly maintains/doesn't damage the property.3.

If rent payments are missed or damages occur, this gives you legal recourse against any or all tenants.Best Practices:Professional property managers, like those managing rentals across North Texas, always screen every adult living in the home.