I revisit notice boards some times and so far no knew quests on ones I've already taken the quests from. I am thinking they do not add new quests once you've taken the ones given by that board, but wanted to check if anyone has seen a new quest crop up on an already-completed board.

No, afaik it's fully static

I haven't seen new quests pop up on there, but there seems to news or info of some sort of things going on in there area

I've had new things pop up on a few boards where I pulled all the notices. They turned yellow on the map again. No new quests, I think but plenty of new POIs.

Notice boards can, and do (not all, though) repopulate. They can also spawn new contracts, though this is not common. As already noted, when a new contract spawns, the board on the map will turn back to yellow.

Thanks a bunch! The board turning yellow again will help.