There are many ways to collect rent. The best is to use an online service. Most property management software has this service available and it's relatively cheap. Rentler is free to the landlord for a limited number of properties.
Most software will also have a place where tenants can submit maintenance tickets and it will keep track of them for you. As far as what they are responsible for and what the landlord is responsible for it really will depend on the lease agreement. Typically, the landlord covers all maintenance. Damage caused directly by the tenant by be removed from the security deposit in most states.
It's a very good idea to require your tenants to have renters insurance. Depending on the coverage it will cover damage to the personal property of the tenants.
I hope all this helps, it sounds like you need a good property management software. Rentler is a good free option, Tenantcloud and Rentredi are other good cheap options.