Is the money I received for going to training in my colleague's car, even though I did not know at the time about the existence of these expenses, permissible or forbidden?

If the amount is disbursed to every attendee of the training, whether it is spent on transportation or not, then the money is lawful (halal). However, if it is disbursed on the condition that it is actually spent on transportation to the training location, then it is not lawful for you, and you must return it to the entity if possible; otherwise, spend it on charitable causes.