questions about shapesharer
No.  Coat of Arms says "Each creature gets +1/+1 for each other creature on the battlefield that shares at least one creature type with it" — it counts the number of matching creatures, not matching creature types.  If Creature A and Creature B share more than one creature type, each one is still a single creature, and they (indirectly) grant each other only +1/+1 through Coat of Arms.  (Also note that Legend hasn't been a creature type since 2004, so Shapesharers don't automatically kill each other.)
Yes, assuming that the Shapesharer itself doesn't have summoning sickness at the time of the copy.  Summoning sickness is determined only by how long a creature has been under a player's control, and turning one creature into a copy of another does not change who controls what.
No (unless of course it's copying another changeling).