No, waypoints aren't spelled out with the ICAO alphabet. They are mnemonics that are pronounced as a word and only spelled out if the person on the receiving end requests it because of bad radio reception, or unfamiliarity with the area/waypoint.
For example, Hungarian waypoints, at least the more important ones are normally named after cities, towns or other geographical locations near them, and use the locations name or abbreviated name, being careful that they can be pronounced reasonably easily for English speakers. Like: ERGOM (for the city Esztergom), ABONY (for the town Füzesabony), SOPRO (for Sopron), etc.
It is, but fixes are almost always spoken as words rather than letter-by-letter. For this reason, they are usually chosen to be somewhat pronounceable, and occasionally you even get jokes in the names. Likewise, radio beacons and airports are usually referred to by the name of their location; for instance "proceed direct Dover" rather than "proceed direct Delta Victor Romeo".
I think a lot of pilots and air traffic controllers would be irritated if they had to spend longer reading out clearances and instructions. In a world where vocal communication is still the primary method of air traffic control, there might be a measurable reduction in capacity in some busier regions.
Disney has a whole lot of special fixes in Orlando and Anaheim. The PIGLT arrival passes through HKUNA, MTATA, JAZMN, JAFAR, RFIKI, TTIGR. I'm fairly sure I've heard about some variants on MICKY, MINEE, GOOFY, PLUTO, etc.
"Fly direct Quebec Xray Kilo Charlie Delta"