20 Sept 2014
Any spell you cast that doesn't have the type creature will cause prowess to trigger. If a spell has multiple types, and one of those types is creature (such as an artifact creature), casting it won't cause prowess to trigger. Playing a land also won't cause prowess to trigger.
20 Sept 2014
Once it triggers, prowess isn't connected to the spell that caused it to trigger. If that spell is countered, prowess will still resolve.
20 Sept 2014
Prowess goes on the stack on top of the spell that caused it to trigger. It will resolve before that spell.
19 Mar 2021
An ability that triggers when a player casts a spell resolves before the spell that caused it to trigger. It resolves even if that spell is countered.