Contracts

We got free phones through AT&T and signed a contract to pay so much per line for so many years.  Now AT&T keeps raising the rate. How can they do that? I signed up expecting to pay X amount per month per line

No you didn't.  You do have an agreement to pay for phones with installments. AT&T has agreed that if you stay for 36 months they will give you bill credits based on you maintaining an unlimited data plan that qualifies for the deal and not canceling your phone lines. 

There have been no service contracts for a decade. Blame T-Mobile. This is their business model. All service providers are following this business model because it works better. It actually works better for the customer as well as the carrier.

 first they remove the discount for auto-pay and then they raised the per line rate.

They did not.  They have made it conditional on you using a debit card or checking account. Credit cards receive half discount. 

Verizon has not allowed credit cards for autopay discount for several years. At least 6 because I've been there customer for 5.5 years.

T-Mobile discontinued the auto pay and paperless billing discount entirely unless you use debit or checking.  

What rights do I have? My phone is not yet paid off.

You can pay off your phone. Unlock it and use whatever service provider you want.

Now AT&T keeps raising the rate.

That's not the case. This is the only time AT&T has raised prices for currently offered plans in a very long time, possibly never. The autopay/paperless discount is up to you.