A: That almost did happen to me once. But I was able to stop it before it was my turn to perform (with about ten kleenex).
Though, if it started when I was actually performing, then if it were small I would just try to sniff it back up best I could before my performance ended. If it became very bad, I would stop and tell the audience I couldn't play anymore. If I were a concert pianist, and I was playing in actual concerts, not just recitals and festivals, then that would be a different story.
B: That's happened to me, in fact, a few times. I just briefly cease playing with my right hand and cover my face so I don't sneeze on the piano and gross all the following performers out.
C: That happened once when I was performing Mozart Sonata K 309 for Certificate of Merit level five, a few years ago. I didn't stop or anything, I just made a lot of mistakes because of it.
D: That has never happened to me during a performance, but if it did, I would probably stop using it and play as legato as I possibly could.
E: I'm not sure what you mean by (keys fall in). But if that is along the lines that they don't work, then I would omit all the broken notes and improvise with all the remanding keys, hoping no one notices. I've had to make up the ending to a few pieces during recitals, not necessarily because the 'keys fall in', but because I forget the piece. Hint: people notice.
F: Once, during the Sonatina Festival, that happened right before my turn to perform. So I rushed to the restroom and barely made it back in time.
But, if it happened while I was performing, well I suppose I would just hold it best I could as that would be my only option.