1.1 no need to check child's credit, but it might be helpful to check his criminal history. In any case their son's identity information should be on the application.
1.2 yes all adults living in the unit more than 1 months should be on the lease.
2.1. yes, it's easy
2.2. yes, use professional company to avoid liability, even if you could have done it yourself with some trap from HD.
2.3. yes, the damage and cost is caused by tenant's actions, and they should pay for it.