http://www.ebay.com/sch/i.html?_from=R40... http://www.ebay.com/itm/4-pcs-New-OEM-Apple-Macbook-Pro-Unibody-Bottom-Case-Rubber-Feet-Foot-13-15-17-/301579648164?hash=item46378c3ca4:g:~E0A... You can just search for them on eBay or amazon, the easiest way to attach them is to just use super glue making sure you don't get any inside the holes on the bottom case.
This screw extractor should work fine: http://www.amazon.com/Moody-Tools-58-0670-Extractor-Reversible/dp/B000JCT3W0 I don't think you'll be able to find those specific screws for that old of a computer without buying the hinge first, but its less than $15 : http://www.ebay.com/itm/Genuin-Apple-LCD-Display-Hinges-w-Screws-MacBook-Pro-15-A1286-Late-2008-2009-/272066404613?hash=item3f586be105:g:N7gA...
From the sounds of it apple is correct and it is the logic board, I have dealt with a few of these, most of them from liquid spills, although apple would have told you if it was a spill when they opened it. I think a new logic board may be in your future.
The most likely cause it the logic board, which is the driver for the backlight. There is one particular part that tends to blow. So a new logic board would most likely be necessary. There is a slight chance that it is the display, but most likely not. If it is the logic board and you replace the display, your new display could be fried by the logic board. But I'm quite sure it is the logic board. A new one will run you about $400, and is a moderate repair for a non-technical person.
I think this is what you are asking, all current MacBooks have a built in "hidden" recovery partition, so there is no need for a bootable usb thumb drive, just hold cmd-r at startup (cmd-option-r for internet recovery if normal recovery won't work). https://support.apple.com/en-us/HT201314 -Brad
Short answer; yes you must replace the entire display assembly. Long answer; technically you could just replace the matrix LCD, but it is very difficult and Apple, nor any other self service center will even attempt replace it, they will just replace the entire display assembly. I would recommend replacing the entire display, but if you really know what you are doing, and want to take a risk it is possible to just replace the matrix LCD. -Brad (Apple Certified Macintosh Technician 2015) MacBook Air 13" Mid 2013 Display Assembly Replacement
What apple said sound like it was pretty much correct, this is (was) covered under warranty (4 year warranty with apple care), the only solution I have is to buy and install a new display, there may be some other solution but not that I know of. Good luck! -Brad (Apple Certified Macintosh Technician 2015)