Multifamily Homes Already Rented Out

[Aaron Lathan]

Thanks in advance if you make it all the way through!

I'm new to real estate investing.  I recently moved from San Antonio to Houston and have successfully rented my first home (using a property manager YAY!)  I'm looking into Multifamily homes both in Houston and in Baton Rouge and several 3-unit & 4-unit homes in desirable areas that I believe would do well and my initial calculations "showed" a great return; state that they're already "fully rented" at a set rate.  

Since the tenants already have a lease with the current owner, is there anything special I need to do to get them re-leased through a property manager of my choice and have their payments routed to me?

Can I change the lease rates if they're a little low for the area?

Many of realtor dot com homes also say "don't disturb tenant"

How do I know the property is not a complete dump?  I don't have the money for major repairs but most of the homes seem to not show the interior.  

I appreciate any advice.