Yes, unlike Daredevil or AoS, ARROW knows how to use its "extra" time & make its episodes one of the Greatest Episodes of Television that will ever be created.
No, his first date after returning from the Island was with Helena Bertinelli (The Huntress). However to be fair, it was never said that this (the date in this episode) was the case in this episode.
Yes, this brilliant & perfect episode does, in fact, showcase the FIRST MISSION of ORIGINAL TEAM ARROW (even though they weren't explicitly calling themselves that at this point in time)