These are considerations a computer will never be able to do!  

I like to play 6.ed5 here - it's more simple and gives black less chances for counter-play (there is no attack on e4 pawn and playing b5 is almost impossible because of pawns on c4 and a4) while white has simple plan attacking d6 pawn with Bf4 and changing quins and rocks on open e-file. Also, white will probably have 2 bishops advantage because the only square for black light-square bishop is g4. Of course, this variant is not winning for white, but it is really stupid to play it as black when he has no any winning chances - it was possible to play 4. ... ed5 and white need to take with c-pawn.

The mistake, if it can be called so, must be in the advance in e6. It is necessary to find a better following for white, after 10... Nh5. What about 11. Nf3, covering the pawn and the queen's check square? Then black can castle, of course, releasing the pressure, but white can too now. Or 11. Be3, so to cover the queen's check with 12. Bf2 (and the black queen must retreat, and white can go on either with 13. Nf3, defending the central pawn and consolidating, or with the poisonous Bxc5, preventing black from castling and still pinning the knight, no matter if black takes Bxe5, since Qe2 will pin it too!)

I think it's all theory for now - it's just very aggressive variant...

Yes, you right! Actually, this is very dangerous variant for black and it's reason why some players don't play Ben-Oni after 3.Nc3, but only after 3.Nf3... I totally forget it in my first comment but it is still good variant for white (4.ed5) if he want play more safe...

It's interesting to note that white cannot play 14. Kg1 in order to release the pin, due to Bd4+, and white cannot take with 15. Nxd4 because of Qf2#. Black can even think about sac Rxf3+ (or not, depending if white has moved the king or otherwise) in order to add his bishop to the attack.

Seems better than the 3 other tries. The position is quite sharp.

Fearlessly. Imaginative move.

But loses after this, mainly because of the black queen's entry on h3 and g2. It seems that the e6 plan must be seriously reconsidered. Hehe, we are doing some opening theory, here... don't you have access to bibliography about this line?

With the unavoidable tempo lost with the queen, black reinforces his pressure on c3 and the game is strategically over. But some mate or massive loss combination is to be foreseen. So is logical the attempt to mix up things with this move, and it has in his sleeve the queen check in a8, slowing down black. The problem is that it is not enough.

Ng4 was pretty a good move, freeing the bishop's action on d4.

would Rhf1 have worked here?

It drops the exchange to Nxh2 discovered check. However I think the position is lost at this stage. I think 12. Kf1 is a losing mistake, but white has had to play well to make the most of his chances.

The rest is just nice to see or a good material for a tactic puzzle, but even in the tiny chanches white could have to survive, it's not a playable position, after which you want to be after an opening. Even if lost, this game is very interesting and enjoyable. If even happens to me to play into this line as white, I'll try to remember "not e6"  )