What to do against early Qf6?

I always have troubles against it. Any ideas, plans?

I'm a bad player but I like 3) d4

Prologue you have somehow managed to become a pawn down with no compensation and in all sorts of trouble. What's going to happen your Bd3 after Nb4 huh?  

Seriously, I don't know how you managed such a good position for black after Qf6, it's actually impressive. b3 is rarely a good move in the opening, a terrible way to play it. 

Play actively. 3 b3 no way!

Take the centre with Nc3 and d4

Nc3 followed up with d4 is the best way to handle both scenarios.

In my opinion, you keep developing and castle.  Then you take advantage of the fact his queen is vulnerable and his knight doesn't have its best square available.  It's not a strong or dangerous move as long as you don't panic into error, for example by entering the Fire Swamp--sorry, Princess Bride reference, couldn't help myself.

Knight can be placed on e7 where it protects against Nd5. In the second position engine suggests Nc3 and d4 but not in the the first one . Knight is covering square d4. So in the first position it isn't clear for me what to do.

In the second position, I agree with Nc3.  Or Bc4.  Just keep developing.

In the first position, Nc3 is also fine.  Or castle.  Just keep developing.  He hasn't got an attack.  He's got his queen on the wrong square which will hurt him later.  For now, just develop.

Wow, MelvinDoucet, that Greco one, I would want NN instead of my name on the other side too.

In your second example, after Qg6, you don't even need your trap since you have Bxg6 (it's a nice trap though, in other circumstances).