When you think of Roman architecture, you generally picture marble columns and villas, or perhaps walls and roads. Did they build any massive stone castles?
The Romans built many great stone forts.
The word "castle" is usually used to refer to the private fortified residence of a noble (though not always, there are Royal Castles, and castles of the military orders as well as the castles of nobility in Medieval times). The Romans did not build many (any?) of these types of "castles".
Some Roman stone forts still exist. Portchester Castle in Hampshire, England, is a well preserved example. (The Roman fort was re-purposed as a castle in Medieval times, and a Medieval stone keep built in one corner of the old Roman fort). The outer walls, built of stone by the Romans were the walls built to create a fort to defend the "Saxon Shore" of Britain against Saxon incursions.
Yes, of course. The great Theodosian Land Walls of Constantinople are perhaps the most notable examples of Roman achievement in fortifications. Many technical innovations in Western castle construction came after experiences in the East, on crusade.