The only thing the Too Solid Flesh (or Flesh Too Sold, if Rose version) Tilt does is take any injuries you suffer in the dream and inflict them on the normal body as well. By a strict reading of the rules, even healing the dream form can't affect the physical body of injuries. So, strictly speaking, removing a stake in a dream would have no bearing on the stake in reality. That said, ask your ST, because they might have different ideas on how things work.

I don't see anything about dream forms not taking the usual bashing/lethal/aggravated damage, so I assume banes apply as normal....