My guess--and I have not read the books--is the former queen-to-be. She picked it up after it fell.
Maybe. I watched that scene again very closely and I think it was probably there to throw us off because it didn’t look like she had the cup in her posession long enough to slip it in with all eyes on her, the cup was empty at the time so nothing to conceal it in, and how would Sansa have known the incident would even happen? It seems the poisoning would most likely be pre-planned.