Rwand Air and Qatar are code share partners, so this should work ok.
Typically the flow is as follows: you will be checking in in Entebbe with Rwand Air and get boarding passes for all three flights. Your bags will be checked through all the way to JFK. All immigrations and customs procedure will happen in JFK.
There will be no immigration or customs in Kigali or Doha, but you may have to go through security again (at least in Doha that's fairly standard). There may also be extra document checks in Doha for the flight the US.
Will this be enough time?
You have a good chance of making it but both connections are on the short side and no connection is ever guaranteed. If you miss it, go to the airline service desk or the gate agent: they will rebook you (for free) on the next available flight and may also do hotel arrangements if needed.
How do I get boarding passes/check in for two different airlines?
Rwand Air should give you all three boarding passes in Entebbe. If not, you may have to go the Qatar Service desk in Doha to get the DOH->JFK pass.
Will I need internet to check in?
It's not a must, but it's certainly helpful. I recommend making accounts with both airlines, associate your reservation with your accounts and installing both apps on your phone. Ideally you check in online 24 hours before departure and then you already have all three boarding passes. Print them out AND bring electronic copies on your phone as well. Most airports do have free WIFI these days too.
Do I go to Qatar to check in and get my boarding passes for all the flights or separately to rwandair and Qatar?
As said before, typically you should get all three boarding passes during your first check in, ideally online from home. There are exceptions, but they will tell you during check-in.
The 55 minute transfer in Doha is on the tight side. You don't have a lot of room for error, especially if you have to go through security, US doc check and potentially to a service desk. It's probably a good idea to familiarize yourself with the layout of the airport, so you don't get lost or take a wrong turn somewhere. Make sure you have your passport, boarding passes, and reservation number easily accessible. If the security line is long, you can potentially flag down a security officer and let them know that you have a tight connection. They can fastrack people.
Have a great flight!