Ooph, 4 questions to find out we know
less about the murder weapon than we thought we knew at the start. There are just over 180 events and 120 conditions in Fellowship block, and if we ask the ideal question and half the pool for each of the remaining question we
come down to... 1-2 cards to pick from. Oh, but we can cut out conditions that don't have special abilities! That puts us down to ~60 conditions and ~180 events. Ideal questioning definitely gets us to an answer in the next 8 questions, and if we're almost-ideal we can still get to it with only 7 questions.
Quick assumptions -- one question to learn the card's side, one (hopefully) for type, two for culture, two for phase, and that would leave us with just two questions to figure out what the card is from there. Doable depending on the culture, but we may also wind up guessing between 2-3 cards at the end. Phase and culture are the weak spots here: if one of those takes longer it'll leave us picking between one of 3-9 cards depending on how unlucky we are. And that's only if this is an event or condition... Aragorn threw Gimli at Uruk-hai, after all

So I think we should leave culture and phase alone for a while, maybe some of the other clues will naturally cause all e.g. Elven cards to fall off the way all underground sites were eliminated by the time we got to guessing if the site was a sanctuary. Card type too, since at the moment if it's an event we only remove 60 cards by asking instead of the ideal 120. And yet, without knowing culture, phase, or card type I'm not really sure what to ask. We can ask something along the lines of "does it place a wound token on a character" but it's going to be really hard to filter down to what that
means without some tuning beforehand, especially after two or three of that type of question.
Side will also knock out either all FP or Shadow cultures and either the Fellowship or Shadow phase, that might be our best bet? Rarity cuts the field into thirds but it's a gamble whether we're left with 1/3rd or 2/3rds of the possibilities. Any other ideas? Even if we do ask about side, what would be a good follow-up question? Culture, phase, and card type would all still be pretty far from halving the remaining cards but what else do we ask about?