Do you also return to the cup all monsters that have the same dimension symbol as the closed or gate?

Good question - I don't know if there is an official answer, but I've always played that yes, the monsters do go back in the cup. Hopefully this is correct, since the last time this came up it was an integral part of deciding which gate to close (needed to clear out out some pesty blockers in the street).

Since a gate is closing, I'd say yes.

Well, I reread the AH rulebook under Monsters and Closing Gates (page 18) : When a gate is closed, all monsters in Arkham, the Sky, and the Outskirts that have the same dimension symbol (see “Monster Movement,” page 10) as the closed or sealed gate are removed from the board and returned to the cup. A monster’s dimension symbol is printed in the lower-right corner of the marker’s movement side.

If a gate closes, the monsters return to the cup. There's no mention that the Investigator has to have an explored marker or anything like that.