Visit the Wargame Bootcamp guild
1 - Nope. You pick one. From the rules - If multiple conspirators or Deputies are equidistant targets, the players choose which one is affected.
The card specifically say "Conspirator(s)", meaning more than one could be affected.
2 - Nope. The Deputy stays put if there is no other "nearest" conspirator.
Where is that stated, as it contradicts the rules about them must move.
For purposes of resolving “nearest”, conspirators currently in the space of the moving enemy are ignored. In other words, when Hitler or a deputy is required to move, they must end in a different location than they started from, regardless of if there was a conspirator in the space they moved from.