Do metros in the US even use the same gauge as trains? Here in Europe they're almost always smaller gauge so sharing isn't an option.
The exception here in Barcelona is Line 1 which is a wider gauge than all the other lines, for historical reasons though it doesn't share any tracks (but lays right beside the train ones at some stations)
For the most part yes. Post below me named some exceptions, but in general the US has done a better job than Europe at standardizing rail gauges everywhere. New York runs at standard gauge, and that alone accounts for about 1/3 of all the metro rail on the continent.
Gauge is basically irrelevant, as the signalling is entirely different between mainline and urban (ASFA/ETCS vs TrainGuard MT in the case you're mentioning, and I have no idea what the FGC uses). Also, urban is typically closed network where the infra and rolling stock are all under the control of the same entity, whereas in mainline that is generally not the case.
It's all over the place. Probably standard gauge is most common, but there's tons of variation. For instance, the DC Metro is slighly (like a half inch) narrower than standard gauge, but SF BART is MUCH wider, something like 8 inches.
