Let's say that I play multi player with just one hero, and let's assume I play Desperate alliance to give the control of my only hero to another player.

I guess I can, due to FAQ 1.7 :

Q: If I give control of one of my heroes to another player with Desperate Alliance (OtD 10) and my other heroes are killed, am I eliminated from the game?

A: No. A player is not eliminated from the game unless each of his heroes is killed. The hero chosen by Desperate Alliance is still in play and will return to your control at the end of the phase.

So what happen if I engage one ennemy, where goes the undefended damages ?

I presume the enemy will place no damage, since there is nowhere to place it... and no rules to direct that damage elsewhere.

Let s say a four player party with one guy playing a solo hero going hammer stroke + desperate alliance, then dwarven tomb or book to replay desperate alliance each turn would work fine ... With ranged characters (for the other players) + allies of your own killing the whole bunch of ennemies whose attacks would be harmless ?

I like the idea. Seems near impossible to pull off with a single hero, but it would be awesome if you did! Don't forget to include Taking Initiative in that deck.

In the French national event, there are bets if someone would dare going mono gandalf to the event .... We are going to play nightmare on the doorstep 4 players ... So I think, you got pretty much the idea of what I want to do.

However, I will have Bilbo every four turns on my side ... Tricky

Thanks to your inspiration, I just threw together a solo Gandalf deck with no allies in it. It would probably be terrible, but now I really want to try it.

Why no ally ? Just to raise the dare ?

Pretty much. If you're going to run 1 hero, you might as well go all in.