In the U.S., people have the right to remain silent during interrogations, so there's no problem with a lawyer advising a client to exercise that legal right. A lawyer can get in trouble (e.g., get disbarred) if they advise a client to break the law, e.g., by committing perjury or destroying evidence.

> Does this change if the person is suspected of having pot or of killing children?

The U.S. legal system has a presumption of innocence, so merely being suspected of committing a crime shouldn't affect the legal rights you're entitled to. (Many innocent people become suspects in police investigations.)