Connected. When you declare an ambition that's not declared, draw and secure the top card of the Court deck. (You can't use its Prelude action now.)
Influential. When you Copy or Pivot to influence, you may influence twice.
Proud. When scoring, you only gain Power if you get first place (not tied).
A: Yes, if you declare an undeclared ambition with a drawn Populist Demand, this ability triggers again.
A: No. Farseers being drawn as a result of Connected does not see the timing window to then trigger its ability to look at a Rival's hand and swap a card with them.