Detached equipment is something intentionally used improperly to impact on a play, and should always result in the minimum three base award.

Doesn't the above apply to batted balls only? Maybe I've confused ASA w/ NFHS. I thought if a play was made with detached equipment, the call was a delayed dead ball and awards of 1 base for a pitched ball, 2 bases for a thrown ball, and three bases for a batted ball.

I also have a question on a catcher's detached mask/helmet.

Batter pops up. Catcher removes mask/helmet and tosses it into foul territory. She loses sight of the ball which:
a) on the fly, lands in the catcher's helmet in foul ground;
b) contacts the catcher's helmet in foul ground and bounces directly into fair territory where it comes to rest.

Is either or both simply a foul ball?

Thanx.

What happens when a batted ball contacts a person, attached or detached equipment or clothing of a player or umpire or any object foreign to the natural ground over or in foul territory?

You are correct. The three-base award only applies to batted balls that are judged to remain on the field. If the batted ball was headed over the fence fairly, then the award is four bases.