In New York City, the trains have ac and they dump the heat into the
tunnels which are well vented.

Not only are the tunnels much bigger than the tube but they are also
much shallower - so that the many gratings in the roadway can be used to
vent hot air.

I really know next to nothing about air-con systems, but I take it the
moisture in the air is condensed somewhere and collected as water - am I
about right?

Why not, then, have a system of pipes on each train, and a big tank at the
end to collect the water, which would be emptied out at various times during
the day (whilst stopped at stations - surely they could implement such a
system?).

The heat, of course, is another issue.

Peter