Steps in mechanism of pyruvate dehydrogenase
The ylide of thiamine pyrophosphate does not ‘form’; rather it is there. There are two major mesomeric structures for the five-membered ring: One including a double bond from nitrogen to the carbene carbon, the other one with a single bond (lone pair on nitrogen, sextet on the carbene carbon). As with mesomeric forms of benzene, the truth is somewhere between these two extremes.

In the carbene elimination step, you seem to assume just by the existence of the arrows that the deprotonation of the hydroxide must come first. That is not the case. In fact, I would assume the first arrow to be the recreation of the keto unit, followed by the removal of the thiamine. Only then would the proton be lost, since we are now dealing with a protonated ketone which is a very strong acid.