What was considered the largest (counting layers, not physical size) cube that was believed to be possile to make until recent inventions?
This is a pretty common misinterpretation. As someone who was part of the twistypuzzles community before the V-cubes were created I know the real story - people knew it was possible to make arbitrarily large cubes (for instance by making the outer layers really wide, or by making the entire thing perfectly spherical) but they didn't because of aesthetic concerns. Few people wanted to waste money producing a very ugly and complex puzzle that might not even work well if at all. I think a few people did try making the 6x6x6, with different mechanisms, but I don't think any of them turned out stable. In those days people were only (mostly?) interested in cubes with equally sized layers, and that was the goal for anyone who wanted to make a bigger cube.
Anyway, it was shown that the 6x6x6 is the largest cube you can make with evenly sized layers - using the standard mechanisms. So nobody believed bigger cubes were impossible, just that they couldn't be constructed with the normal technique (a bunch of plastic pieces and a core held together internally by their shape, with any layer able to turn without affecting other layers) and with even cubical pieces. People thought bigger cubes should be possible using magnets (the c4y guy made a 9x9x9 out of dice and magnets) or other things like that, but few people were interested because of aesthetics. A modder named Etienne de Foras made an even-layered 7x7 using a new technique where turning one layer would push out pieces on neighboring layers, much like the Floppy Cube, but I don't think the idea was ever made into a fully functional stickered cube, even though pictures of the almost-complete cube exist.
To me, the big invention of Mr. Verdes (apart from the great mechanism) was not the idea that bigger cubes are possible, but that the pillowed shape is a good one. Everyone assumed a perfect cube would be better and didn't even try to look at other alternatives; when Verdes first showed off the V7, people finally began to realize that the pillowed shape was both pleasant to hold and more stable. For a while after the worldwide V-cube release, many builders transformed smaller puzzles (3x3x3, 5x5x5, megaminx) into pillowed versions.
When & where was the first WCA competition?
This might be a tougher question than it sounds like. The WCA was definitely not around in 1982; that competition is accepted as official retroactively, because the results are all well-known and because it had been advertised as a world championship which gave a good inaugural world record (i.e. the Gunness world record) to compete against. I believe that faster times than 22.95 had been achieved in competition by 2003 - the fastest I have heard of was a 17.02 by Robert Pergl at the Czechoslovakian Championship 1982. Anyway, I don't think the WCA was even around at Worlds 2003 - I wasn't around then, but after asking around it seems like the WCA was actually created (as an organization) around mid-late 2004. So asking what the first real WCA competition (WCA-official, after the creation of the WCA) is is not at all a trivial question. Perhaps it could even be categorized as a trick question, as the answer is certainly not what most cubers would suspect.
EDIT:
Well I read somewhere that "The number of unsolved configurations on a Rubik's cube is a prime number."
43,252,003,274,489,856,000
Umm... no.
Subtract one (for the solved position, right?). Now it's prime.
