Buying home already with tenants - need help

[Ben Kirchner]

So I am closing on this house in a month.  The current tenants have lived there for 7 years, and were paying $750 a month.  I originally thought the $1100-1200 a month I would require for rent would have me looking for new tenants.  However, they are okay with paying $1100 on an 18 month lease.  This saves me the hassle of locating a tenant myself, or the expense of hiring a company (like I usually do) to find a tenant for me.  However, I have some questions that I'm sure experienced landlords can help with.  

I'll start by saying the tenants are hispanic.  One speaks pretty good English, but there is a bit of a language barrier that makes some things unclear when communicating.  In addition, none of the tenants have a computer, and therefore anything needed to do online becomes a problem for them.  Lastly, 2 of the 4 adults living in the house only get paid cash, and do not have a bank account.  

Am I making too many concessions?  I feel the fact they have been good tenants for 7 years (with 3rd party verification) offsets a lot of this.  My questions are what methods would be recommended for:

With them not using a computer, what methods would be recommended for application, background/credit check, income verification?

As the person buying this house on 12/1/17, I need to make the decision on if I wish to continue to allow these guys to be tenants, or give notification that I want the house vacant by closing.  By not giving notification soon, it will be on me to get the current tenants out, rather than the seller.

I appreciate all input and advice.

Ben