Yes it was. The fact that they used a Lancer Evolution shell is irrelevant, since touring cars and rally cars are built using the shell of a street car.
Yes you can. I know several companies that sell touring car engines (fully built) to outsiders. Circle track racecars all use off-the-shelf parts. Except at the highest levels of racing, many teams use off-the-shelf parts... and sometimes manufacturers and tuning garages sell fully-built racers for specific events. This encourages privateers to enter the sport.
Now you're just being silly:
The CT230R is built specifically to compete in Time Attack competitions. Which are timed races. And as timed races, they issue racing numbers to the cars. (Wow!) Thus, it's a race car.