After reading the rules online I have three questions:
2. When terminating another player, can you pay the three knowledge tokens from the ones you achieved from terminating (if you didn't have three tokens before you terminated that player)?
The answer to 2 is no, you can't use what you would get to pay for terminating someone. The rules specifically state (pg. 22 of English version) that "...you must discard X knowledge tokens" in order to take that action. So, if you don't have the knowledge tokens to begin with you can't take the action.
For the first question, I don't see why you couldn't. For the last questions, I'd like to know too.