In regard to the repair, have a look here
[guide|18027|Kindle Fire HD 2013 Teardown]
Probably the best you'll get for a guide at the moment
in regard to a screen, you'll need to hunt eBay, pretty much the only way to get kindle parts is from pre-used kindles. The problem is the age. you need to find someone who has a broken kindle but a working screen they can sell. because these are all still under warranty. if an internal part fails Amazon will replace it.
You can set up an eBay search for the part and in advanced search you can set eBay to email you new results as they come in every day.