OP, sorry someone tried to open some accounts in your name. Thankfully you were able to catch it.
As for your new car, first, congrats! Buying a new car is always fun...at least for me. Now, as for the running of credit...do you have any pulls from Toyota Financial? If so, I wouldn't worry too much. If you don't and the dealer insist that you unlock EX it could be that he hopes to hang your deal with Toyota Financial but I'm certain he has a backup plan in the instance that you don't or can't.
The dealer has NO incentive to take that car back...trust and believe any good finance manager will have another card to play. You'll be fine. As for the delay, well if his intent is to hang your deal with Toyota and for whatever reason he can't then he'll hang you with someone else and there may be a re-inking of paperwork and possibly a change in rate.
Don't worry about it too much...just focus on enjoy your new car! Congrats again and enjoy!