Correct.
Wrong. Twins are allowed to run up to 1000cc - Ducati 998. Triples up to 900cc - Benelli Tornado. Fours up to 750cc - Suzuki GSX-R 750.
The TLR is a Suzuki, its Japanese. Not a very popular twin due to is relatively wide girth, heavy weight, and experimental rear damping system which was promptly forgotten about by Suzuki. It was one of the reasons the TLR didnt compete in World Superbike (hard to set up).
There are lots of cheap Japanese V Twins. The RGV 250 (two stroke) is really the only quick one as far as I know. Rode a VTR250 (honda) very nice bike, slow but. Owned a GSF250 Bandit (suzuki) inline 4, 20,000rpm nakedbike but also slow (quicker than the VTR though). CBR250RR is the weapon of choice for young blokes. 20,000rpm + cheap. Aprilia RS250 would be my weapon of choice with the quickish RGV engine, and italian suspension/chassis. I think the 125 would end up leaving you wanting. Keep in mind though, that everything happens over 9000rpm on an RS250, fantastic through the twisties. Mixing oil everytime you fill up would be a pain, but the payoff is power. Get a cheap CBR250 so that if you crash it, its cheap to repair, then shell out the big $ for a 600cc when you want to upgrade.
red17, its quite obvious you have a vague idea of what you are talking about, but please dont post advice or "facts" when you really haven't got a clue.