When translating from English, "the board" without a context could be a wooden plank, but that's not what they mean here!
Earlier we were taught that "o conselho" means advice. And now it means "the board"?
It can mean either advice or board as in a board of directors.
Yes, it can. But you should specify:
O quadro de diretores or o quadro de executivos.
It also can mean,
The board (group) of some professionals such as o quadro de professores / policiais / trabalhadores da indústria and so on.
The board (group) of some workers at a specific department in public service or at an organization of any kind. O quadro de engenheiros / analistas / estagiários / vendedores and so on.