I think Bryan's suggestion of a "Tavern" in town is a great idea. However, the new character would have to start at the lowest XP which will make players really think about their party makeup at the start.
I don't think they would. At least when I play the game (off-App) I always allow people to join in or out between the missions if the player count allows it. In quest wise I think that they meet a new hero while on the town and then take that into the group. There is nothing in the rules that say the new hero has to start from 0 XP. So I give the new hero the XP that would have been aqcuired during the earlier missions.
I cannot see why the app hero changes could't have this same rule.