I have some questions that are just sitting there, for which I either don't agree with the answer / it doesn't work for me. Can I not delete a question once someone has posted an answer?
You cannot delete a question if it has answers posted to it that have at least an upvote.
It's disabled because deleting a useful answer to an on topic question deprives the community as a whole.
If the answers do not work or solve your problem, you can comment on them and/or downvote them to signal to other users that the current batch of answers do not fit/work.