1. a) Can you play an event or operation card that cannot be fully resolved? For example, playing a with only two cards left in the stack or playing an with no cards in archives. Precedent set with tutors leads me to believe the answer is yes (as you can search your deck for something, fail to find it, but then still be required to shuffle your deck and trash the tutor).
1. b) Are there any limitations to (a), and if so can you give me a list of the game functions that can force an operation or event to be unplayable if said function is impossible. For example, a list like so:
- Search for a card: you can fail to search for a card if it is not in your deck, but this does not prevent you from playing a card that searches for that card
- Drawing cards: you can fail to draw cards if there are no cards left in your deck, but this does not prevent you from playing a card that draws cards
- Choosing ice: you can fail to choose ice if there is no ice installed, which prevents you from playing a card that requires an ice be chosen
And so on for whatever that list looks like.
This answer gives a rule of thumb for determining whether or not an action or ability can be triggered: "If a prevent/avoid effect would do something to this effect, then it can be triggered. Otherwise, it cannot be triggered."
This ruling directly contradicts the Activate Blank "When Accessed" Ability Ruling.