Do bow and longbow arrows work with crossbows and do crossbow bolts work with bows and longbows?

No and no.

Specifically, arrows for bows are longer and more flexible as a slight flex can improve an arrow's flight, but crossbows would be too powerful and break the arrow.

Crossbow bolts/quarrels are far too short to be used correctly in a bow, as a real archer would never partially draw the bow to shoot an arrow, yet a bolt would not be long enough for the archer to draw back to his or her anchor point (that same place on their face they always draw back to, to make shots powerful and consistent).