Some cards like The Red Viper has the ability not to kneel to attack. Assuming that the character is already knelt due to AGH or some other effect, can he still declare challenges to attack while knelt?

No, you can't.

The fact that Red Viper can attack without kneeling does not mean that he can attack while he is knelt. The Red Viper must follow the normal rules in order to be declared as attacker (or defender): he must stand.

There are character, like some Clansman, that can attack while kneeling, but it is an exception and it is specified in the text of the character (the same way it is specified that the Viper can attack without kneeling if you attack a player with less character than you).