Given his mental instability is there a chance Trump will launch a nuke at some errant country so he could stay in power?

Iran? North Korea? China?
Remember, he still has the nuclear codes.
He needs to distract the public from his recent disastrous performance. What are the odds he will do something even more disastrous in desperation?

The odds are not zero. Up until yesterday I would have said the odds of dissidents storming the Capitol were zero. Surprise!