So when I use a sword that has a prerequisite of Dexterity instead of Strength, does that mean my Dexterity is also used for damage bonus calculations? Or is that still tied to Strength?

I prefer hand-to-hand, but I would try a Dex archer type character, so long as I still could at least be decent in hand-to-hand.

I have a similar question which may also fit into this thread.

How about the crossbows? Usually they have a strength prerequisite. But how is the damage calculated, based on strength or dexterity?

no yes crossbow is based on dex

it was always the same in gothic and risen.