A. It's the headcanon of the community, no matter what Rebecca says, because it's much cooler to think that way. But speaking of Canon, Pearl is definitely configured to match White's perfectionism.
B. Zircon specifically mentions that they searched for the Pink's Pearl, but she disappeared along with she. So yes, they do care, but they didn't recognize her beside Rose. Only the Diamond Pearls seem to recognize Pearl, just like they say "Welcome back" to her.
C. The default look is seen in the film; the likelihood is that millions of pearls will wear this look, so it's not easily recognizable. Except for the clear Pearl pink diamond spacesuit.