Trap feat! Taking Daylily as the example...
A) With two strikes, Daylily averages 20 + 20 in damage. Normal Vital Strike is an average of 27 damage. Maxed Vital Strike is 37 damage. So, it is a gain over the normal vital strike of 10 damage. But it is still not as good as if he can take two swings.
B) Rage ends. Daylily drops 15 HP. In a toe to toe, trading damage, the 10 damage you gained against the opponent is offset by 15 HP that you dropped yourself on the first round. The second round, you are +20 damage vs the 15 offset. Do fights get to third rounds with barbarians? As Daylily goes up in levels, that drop in HP is an additional 3 per level. It is, in my opinion, better to maintain the rage.
C) When the rage is off, an AoO is a normal or fatigued attack causing you -2 to hit and -3 damage.
D) The feat only applies to Vital Strike. Not Improved Vital Strike or Greater Vital Strike. The Improved and Greater versions do not "add to the base feat" but specify from ground up the feat's ability. As soon as you can take Improved Vital Strike, the 10 bonus damage drops to 3 bonus compared to using IVS straight and maintaining rage. Verses the Greater Vital Strike, GVS is ahead by 4 instead. That makes the feat pointless to use once you have GVS.
So, it is a short term feat that loses effectiveness if you continue up the feat chain where it doesn't apply.
The answers you wanted, which are my opinions:
* If you have Tireless Rage, Yes, you are still fatigued.
* Human's Heart of the Fields would allow you to ignore the fatigued condition causing effect once per day.
* No, you are not fatigued if you have immunity to fatigue from a lame oracle. The feat does not say if overrides immunity. As far as I know, nothing without an "Epic" rating overrides an immunity. A BAB=+6 feat does not qualify as epic.
But it is still a short sighted feat.

D) makes it pointless to take if the campaign is going into the higher levels. In PFS, where you retire at 12th, it has its uses.