1) Avoid setting up in terrain. The zoanthropes aside, there is very little shooting and certainly none which beats your armour save. Receiving a unit of ymgarl genestealers unexpectedly in the back, however, is a lethal experience. The lictor isn't too much of a threat to a decent size unit but is more than capable of charging out and smashing up a tank if you float too close to area terrain.
I'd consider keeping the warrior in a ghost ark. The doomsday ark's mega-cannon-of-doom isn't actually that great against the tyrant - the achiles heel of blast weapons vs monsters is only doing one hit at a time and - more importantly - a swooping monster can't be attacked by blast weapons.
Herm_777 is correct in that the tyrant is your priority kill number 1. If it deploys hidden somewhere, it will swoop forwards 24" on turn 1, then glide 12" on turn 2 and charge. That is realistically enough to hit anywhere on the board save the back edge after possibly only a single shooting phase with snap shots only, and, biomancy or not, it will chop any unit you put in front of it into itty-bitty dog treats. The testla barge is the closest you've got to a hydra, and is a good call.
The night scythe is fine - the hive tyrant won't be able to hurt it, and nor will anything much else, so long as it doesn't slow down. Tyranids have no skyfire weapons and virtually no way of getting them, and vector strike at S6 (base strength, remember) won't do much against armour 11. There's no real point in putting a unit inside - all it does is deprive you of their firepower on turn 1. Mobility won't help you that much - you don't want to get closer to the bugs - with the possible exception of late-game objective grabs. For these, though, there's no need to start on the plane.
To my mind, just take a doom scythe for extra shootiness and use it as a gunship. Prime target are the tyrant (if he's still alive when you arrive) as the scythe can skyfire its guns, or else the shrikes (winged warriors) because 3 wounds each makes them hard to bring down with small arms fire, but dead meat the moment a death ray touches them.
HQ wise..... first, don't bother with obyron. He's the best combat HQ necrons have but largely relies on the combination of a 2+ save and an AP2 weapon that isn't unwieldy. The problem is that all monstrous creatures, rending hits and boneswords will go through your armour, so there's a pretty good chance he'll still get junked before he attacks.
Zandrekh - not bad, but there are relatively few rules on the list tyranids are dependent on.
Trazyn is good, if only because a bug army has no sergeants, etc, and with a tervigon on the board you may find yourself buried in swarms. When facing lots of big units of fearless but largely useless and easy to kill military detritus (like termagants), Trazyn's empathic obliterator is worth its weight in gold. In addition, he'll make a deathmark unit scoring, which could win you the game.
Mindshackle scarabs are a good call on non-special characters and/or courts for special characters. Not to put too fine a point on it, it's the only way in hell they'll survive a challenge against a monstrous creature.