Well, I was searching and found this to help with your first and second question.
>The Shadow Triad (Japanese: ダークトリニティ Dark Trinity) are the faithful servants of Ghetsis and N and are high ranking members of Team Plasma.
>The Shadow Triad are completely loyal to Ghetsis because he once saved their lives.
Hmm, so apparently they are totally loyal to Ghetsis because he saved their lives. So they want to repay him by joining Team Plasma or protecting him, perhaps. Ah, these quotes may explain things:
>"... ...You, huh."
"Ghetsis is gone. He went off somewhere alone after we rescued him from the castle."
"From the day Ghetsis saved our lives, we have sworn to be loyal to him. Even now, after he ordered us not to search for him."
About your last question, I found a terribly vague fan theory:
>There is a popular fan theory that they are the Striaton Trio; this is not true because in the flashback A Triple Team it shows the Striaton Trio battleing the Shadow Triad.
Basically it says that the three Shadow Triad members are Chili, Cress, and Cilan but it isn't true because if you do memory link you can see them battling each other.
Source 1, Bulbapedia
Source 2, The Pokemon Wiki