Welcome to ITST! Lets answer your questions:
jokkemannen wrote:I've understood that you can't play carreer with the itst mod. Is that correct?
Yes, that is correct.
jokkemannen wrote:- Can I play a simple tournament against the computer with the itst? If so, how? Or can I only play online tournaments?
ITST Mod has been developed for online gaming. You can play matches online and ITST Tournaments are played online against other members of the community. You can sign up for tournaments here:
ITST Tournamentsjokkemannen wrote:- How do I join online tournaments? I would appreciate detailed descriptions since I am very new with this game

See above.

The Draw for the tournament will be released on the date the tournament starts. Then you know who your next opponent is. You contact him via Private Messages on the forum to schedule the match, that is, you tell your opponent when you can play the match (important to indicate a day and a time, like Monday 8 PM CET until 11 PM CET). Then you meet on ITST Chat:
ITST TE Chatjokkemannen wrote:- How do I create a player who I can improve ahead of the online torunaments?
Tournaments on ITST TE Tour are only played with the players given in ITST Mod. The stats are fixed and there is a so-called CRC Check guaranteeing that stats have not been altered.
jokkemannen wrote:- Can I switch back to the original game without the itst so I can play carreer mode whenever I want?
It is best to have two installations of TE on your PC: One with ITST Mod and one without it.