Keys falling off Retina MacBook Pro!

Question

Since around 6 weeks ago, my MacBook Pro's keys have been randomly coming loose and falling off. Currently as I try to type this, I am missing my F1, F2, F6, Backspace, Backslash and Spacebar keys.
For a while now, I've been popping said keys back on and now because I've repeatedly snapping on the keys, all said keys will now not attach to the keyboard and stay on there because tiny little clips on the key caps have broken off. As well as my F2 and F6 keys snapping in half whilst trying to put them back on.
I don't know whether this is related to the key issue, but just before this started happening, something very odd happened with my MacBook.
One night, I went to bed and closed my MacBook and it went to sleep. The next morning, I went to go open my MacBook and the entire computer was so hot to the touch that it burnt me. There were no fans, the screen wasn't on, the computer was just ridiculously hot. Before I closed my computer, I quit all open applications and there is nothing (to my knowledge) installed on the computer to have it wake up and heat up to dangerous levels. When I finally opened the computer, the fans sped up to full capacity and it froze randomly every minute or two for about an hour. After that, it's been running perfectly. The computer wasn't on charge.
Will Apple replace my keys under warranty? It's a massive inconvenience to have missing keys as I start an Advanced Diploma course next week and I *NEED* my computer working perfectly.
Regards,
Aidan.

Answer 1

Thank you for your responses.
As I don't have an actual Apple Store in my state, first I'll try and take it to the retailer I bought the MacBook from and see what they can do for me, and if they can replace the unit on the spot. I'll explain to them it being a retina model and it's unserviceable nature and hopefully they'll respond happily to it, JB HIFI (Australia) are usually good with this type of thing. I've also taken out a 3 year extended warranty with them when I bought the laptop so I think I need to go through them to continue to have the warranty honoured.
Since I can't be without the laptop for more than a couple of days, if JB HIFI won't replace it, my next step is to take it to a certified apple repairer and see if they'll offer a replacement. I've had a closer inspection and on a few keys which have broken, a few metal hooks that hold the "scissor mechanism" in place aren't there where they're supposed to be which makes me believe this could be why they're falling off and not staying there.