No. Largely because, without any clear evidence in the Bible, there is no reason to do so. Vegetarians were not that common in that world save for the odd group like the Pythagoreans or Essenes (and I'm taking your word that they were vegetarian, I have not done much research on them myself) so it was unlikely. Had he been a Hindu preacher in India, it would be more likely.
Depends on how you understand the meaning of Easter. For me, it is about the renewal that comes with resurrection (a spiritual, rather than physical process, for me) and I don't think that what Jesus ate for dinner makes much difference in that interpretation.