Ok. So you can only sell stuff that is not untradable? That kinda sucks. Also found a notorious monster the other day. I didn't know what it was or what lvl because it said "??" so I tried to look it up on here but not a lot was given on it and almost died when I saw the health bar move but was still full. That was crazy.
Untradable gear and items (generally "Bind on Pickup" in other games) are far, far, far less common in FFXIV than they are in most MMOs, so it really shouldn't be a huge issue.
Those onyx tears were given to you from the Grand Company, it's basically a small elixir. Restores some hp and mp, just use it in a tight spot, no need to sell it. Almost 90% of the other things you get daily are tradable.
As for Notorious Monsters, they're usually significantly higher level than the surrounding enemies. Unlike rare spawns in most games, where they're pretty easy to kill, and just have a chance at some random loot, Notorious Monsters are tough, and drop a loot specific to them. As a rule of thumb, a full party of players that are about the level of the surrounding enemies is required to kill an NM. There are lots of exceptions to that rule though, of course.
Steer clear of NMs until you've got a foothold in the game.