Is it worth?

If you're really desperate to give your Nino Fury, sure, go for it, but your feathers will suffer a lot.
But if I were you, I'd wait to get a Hinata (even if it gets really long and boring) 3* or 4* to not spend my feathers away.
If you decide to wait to summon for a Hinata or an Eldigan 5*, I'd recommend you to have a team to support your Nino for the time being.

I would just use a different skill. I have Swift Sparrow on my +Atk Nino, but before that I had Darting Blow. Put Fury on once you get Hinata. Don't waste feathers for Fury.

No.

Fury 2 will be fine until you pull a Hinata.

Definitely not. Fury 2 will suffice until you get lucky enough to pull a Hinata.

Fury 2 will be enough, I put it on my Nino +spd -def Nino and it's more than enough.

It depends on your situation. I've upgraded a Barte for Fury 3 SI and I didn't regret it. I've also pulled a lot of Hinatas. But you have to ask yourself which would help you more given your current roster of heroes and how badly you need that extra +1 to each stat on Nino. And how much is merging Nino worth to you - because you're likely passing on a merge to get Fury 3.

Nah, fury is nice, but if you can't get a Hinata, go with something else like death blow, darting blow, or life and death.