No. Putin is not crazy; he knows it would be stupid to do so.
Recent events have... not been kind to that theory. Putin certainly seems off. Nothing about this invasion makes sense strategically, and that was true even back when we thought it would be executed competently!
From what I've seen, he may be the most delusional human being alive.
Does not have to be the case. If the loyalists around him don't topple him he can sell this one way or another to the Russian public. I think a lot of people outside of Russia think it's some heavily censored, propaganda-fueled place. Most Russians are actually very skeptical of what their government says, it's very common to roll one's eyes at official statements. However, this does not change the wish to remain powerful even if just in a self-preserving image. If that does not work, the victimhood card also is often used successfully. If Putin can remain popular and the cronies around him don't replace him it would not have to be over for him at all.