Lying to the cops is considered obstructing justice. Lying to the Feds is a felony. Don’t talk to them, don’t tell them what you think. Let your lawyer tell them what you know. If you don’t know anything at all about the issue, then fine, say so.
Close. Under some circumstances, I suppose that a lie could be “delaying or obstructing” but it’s the obstruction, not the lie itself that is illegal. A fine distinction, perhaps, but material.
You are quite correct that lies told to federal agents are themselves crimes under federal law. You’ll look long and hard to find a similar state law that applies to your local constabulary.