1) Yes, wait.
2) True at higher levels (where you can keep both ball bags "full" and a ball-person brings out the new balls when you request them. At most HS and below games where you have 3-5 balls for the entire game, it's not as big a deal, especially if the ball fouled to the screen is the "last" one. If you still have a couple, then have the on-deck batter bring it to the plate when he comes to bat.
Both, especially the latter, are soemwhat area dependent -- much like someone calling the umpire "blue" instead of by name.
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