Hi,
Corsair Eldar are a top of the bill fleet. Your fleet selection is pretty solid and good. One thing I would change is dropping the Shadow and add more escorts (2 Nightshade & 2 Hemlocks to get 9 of each = 3 squads of 3 per type). Add re-roll for remaining points.
Such a fleet will last, depends on the fact how hard you destroyed the opponent if the battle ends after turn 2.
Yes, Eldar play different, not advised to beginners. With Eldar you'll learn to play Eldar, not Battlefleet Gothic.
Tactic wise? Be a git. If hiding is needed : do so. Even if this means six turns of none shooting. Make your movement & placement count.