And none of your party members in all three games or other guys, who fight against darkspawn, e.g. the whole army in the battle of Denerim, is infected by the corruption of the darkspawn. In "The Calling" everybody has to use a special antidote to survive the fights.
Yes because in order to be infected contact with fluids like spit or blood is necessary and Morrigan was very much bitten by the red Lyrium dragon.
Also there are many at Ostagar who were infected
Cast of DAO:
The warden=can't be infected because is a GW
Alistair=Can't be infected because is a GW
Loghain=Can't be infected because is a GW
Shale=Can't be infected because is a Golem
Leliana=Can't be infected because is blight resistant
Sten=Qunari with dragon blood resistant to the taint
Wynne=Mage abomination healer protected by a spirit who as a mage don't fight the darkspawn in melee
Dog=If not of HN origin is blight resistant and probably even the human noble dog got the flower off-screen when he was with Duncan
Oghren(non DAA version ),Morrigan and Zevran are the only one who are the exception here but since Oghren is an expert against the darkspawns being a dwarf of Orzamar i can expect him to resist the infection like most dwarf of the warrior cast.