The Romans were way ahead of their time in terms of construction ability and plenty of the stuff made much later is downright crude by comparison.

Construction techniques aside, what was siege technology like in the Roman era? Did they build walls to resist heavy thrown rocks, or just arrows and infantry?

Siege towers, battering rams mostly. The most effective siege technology was probably hunger... crude but quite effective.

Oh and this is another thing they brought to bear on cities unwilling to bend to the Roman boot (or Sandal):

https://en.wikipedia.org/wiki/Ballista

and even more here:

https://en.wikipedia.org/wiki/Greek_and_Roman_artillery

Not as effective as taunts and cows, perfected by the French.

https://www.youtube.com/watch?v=ey0wvGiAH9g

Catapults and other torsion where during the Roman empire, though the thickness of walls also related to how tall they needed to be to be effective. Anything under 30 feet is easy to get over using simple ladders.

The Trebuchet is plenty old enough, but we don't have evidence of use by Rome.

As far as I know, it depends on what you mean by trebuchet. Counterpoise trebuchets (using heavy weights) are definitely medieval.

Yes, the giant weapons most people think of when they hear the term trebuchet is medieval improvement allowing people to further scale up the design. A mangonel (traction trebuchet) is the older design, but trebuchet is referring any scaled up staff sling.

Greek and Roman catapults were lighter than medieval trebuchets, using tension or torsion springs rather than heavy weights, but were reasonably capable of hurling rocks well enough to take down a wall eventually. I don't have an example offhand, but the Romans were more than happy to build thick walls to resist sieges if they needed to. My impression is that, fortification-wise, Romans preferred walls and ditches rather than single highly-fortified buildings like castles.

On the other hand, Roman architecture was such that they did not need very thick stone walls to support high buildings.

I think we may all be assuming that the round foundation necessarily means tower, when it could just be a round room. Any ancient Roman architecture experts care to weigh in?