A rather lengthy strategy concern...

[EricH]

I'll answer as best I can.

Originally Posted by master_nickz

1. Regarding scoring...
We have some ambiguity regarding the entire scoring process beyond simply the points for various achievements. For instance...
a) If a team from the opposite alliance is in the process of herding of our alliances's game piece and they accidentally bump our ball across our home zone, do we get the according points as if we had herded it across ourselves?

Yes. <G08> (and the term is finish line).

b) What happens if a team on our alliance has possession of our game piece and drops it after part of their robot, even if just a bit, has already crossed our home zone? Do we receive any points for this?

If the trackball has already crossed, no. <G10>, first sentence. Also see this Q&A.

c) Does the game piece have to be removed from an alliance's overpass for them to qualify for the 12 point bonus at the conclusion of the game? Or is is it a legitimate bonus if a ball simply sits on top of an alliance's overpass for the whole game?

No, it doesn't have to be removed. I tried to find the Q&As on this, but couldn't, but <G14> makes no distinction as to how the ball got there.

2. Regarding aggressiveness...
a) Can a team from our alliance knock a game piece from a member from the opposite alliance if they have possession of their own game piece and we manage not to get tangled after attempting such a maneuver? Would this result in a penalty? If so, how severe?

That depends. If they are trying to hurdle (<G42>), no (10 point penalty). Otherwise...follow <G37> and you should be OK. This one depends on the ref crew, though.

b) Can a team on our alliance block a robot on the opposite alliance if their team does not have an intention to pass us? For instance, is it legal if another alliance is close to their home zone and they are attempting to shoot a game piece above their overpass and a team from our alliance attempts to block them by idling in front of them?

See the definition of impeding in 7.2. That is a legal move on blocking the shot (provided <G42> isn't violated), but you do risk an impeding call if there isn't a clear lane or they ask to pass you. Another one to be careful on, as it may depend on the ref crew.