By RAW, yes. There’s only one kind of crossbow bolt listed in the equipment section of the PHB.
Pretty much. There's the "when does worrying about such minutia actually add to the game" litmus test. Most of the time it doesn't.I can handwave found armor fitting perfectly, so crossbow bolts don't even merit notice.
All those casters get unlimited cantrips. You should let the martials use bolts interchangeably.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.