Is the only requirement of the medium for it to be a salty fluid or is there something else I'm missing here? What even is the funny-tasting brine they sell buckets of feta cheese in?

Depends on the salinity of tears, which I do not know off-hand. What I do know is that brine is a specific salinity of water - saltier would be salt water, and less salty would be brackish water. I would suspect tears are probably brackish. I'd open another tab, but that would require shifting in my chair a little bit to move the mouse more, and I don't want to do that right now.

I think the funny tasting part of fresh feta cheese brine is just cheese juice. I kind of thought the juice tasted kind of how cheap soap smells, but fuck if I know, I've only bough the fresh stuff from the Arabs.

Well each tear contains diffrent amounts of solutes ,depending on things such as what caused the tear,and tears also contain things such as oils and proteins ,but on average ,each tear contains about 0.75-1.1 grams of salt to everything else ,which is about 68.2% ,while brine contains at most ,around 30% salt ,but you must remeber that ,like I mentioned before ,tears contain other solutes such as oils and proteins.

I am not yet a pickle, so I can confirm that you cannot.