well, this is an interesting subject.

i can only really focus on the european area. I will point out, we have found very few "full" siege engines. if used in a campaign, they usually didn't wheel them around, they took all the metal bits off and moved one. Then when they needed to set them up again, they found some wood and remade them(atleast the romans)

The giant crossbows are called ballistae - there are actually a few varieties of these and a lot of images that may or may not be accurate.

• these were primarly anti-personal. They did not have enough power to go through walls. They were great at sticking people though. The bolts were the size of a broom handle, and were able to atleast go through the first shield and guy in a shield wall. That guy, shield and bolt became an problem and broke down a bit of the effectiveness of the shield wall and hindered mobility.

catapults/trebuchets are a little different. there were smaller catapults which were more used for anti-personal because once again, they wouldn't do a great deal of damage to any real walls.

now, trebuchets can be huge and we used for sieges to damage walls mainly and maybe harass/kill the defenders/attackers.