This is a known issue, and a fix is coming.
Symptoms
Apple is aware of rare circumstances where the built-in keyboard and
Multi-Touch trackpad may become unresponsive on 13-inch MacBook Pro
with Retina display (Late 2013) computers and is working on an update
to resolve this behavior.
Resolution
If you experience this issue, reset the keyboard and trackpad by
closing the computer’s display for approximately one minute and then
open it.
Sources: MacRumors.com, Apple Knowledge Base
Yes, it's possible to replace individual keys without replacing the keyboard.
I recently replaces right SHIFT, right OPTION and several f1 - f12 keys on my 2011 13' MBP. SHIFT key was chipped on the bottom edge, which made it unaesthetic. OPTION fell off. I customized my fn keys with Karabiner, so the symbols on them no longer apply.
Mechanically, the replaceable bits come in two parts, the cap, which is black and covers all you can see, and the clip, which is white and lays underneath. The part where the cap holds onto the clip is most fragile. There are instructions about how you pop the cap. I say you should be prepared to replace a key if you decide to pop it, since, especially for first timers, removing the cap might damage the key irrevocably.
I decided to replace my own keys because 1) my machine is outside of warranty, 2) a professional would only replace the keyboard as a whole and that costs way more than buying a keyboard myself, 3) replacing a keyboard myself is a big project that requires gutting the entire machine.
I used a Chinese ecommerce site. The parts cost less than a dollar each. I'm sure you can use ebay. One big caveat is that you should send the seller a picture of the cap and clip you are trying to replace. Even in machines with same spec, the keyboard can be different. A fraction of a millimeter difference could mean whether a cap and clip can fit onto the existing keyboard.
Best Answer
No. Impossible.
You can pop out the keys if you like (see this YouTube clip). I would advise against pulling out the entire keyboard as you won't be able to clean it any quicker and may damage it (depending on your dexterity) in the process. It is also a lengthy process that requires removal of the logicboard (hit up iFixit for details). Technically, the keyboard is attached to the top panel of the notebook (unlike the pre-unibody MacBook Pros).
As for a cleaning solution, you can use any monitor cleaner or a high concentrate (99%) isopropyl alcohol (70% will if you can't find the 99%, but not preferred). Apply it using q-tips or a small micro-fiber rag.