Does the armor Dex penalty applies also to the Dex roll for avoiding knockdown?
I think not....otherwise all the knights would go around without armor! (and this is awful...)

No, it does not. I think it is stated explicitly that the DEX penalty doesn't apply to the balance rolls that are triggered by the Knockdown.

Well, not so explicit, but still:
"Encumbrance is not used to modify a DEX roll for balance unless the Gamemaster decides that it should, based on the circumstances."

The consensus is that Armor does not modify DEX rolls for the balance.