Often, yes. Raffles are regulated as a form of lottery almost everywhere, and in the US the rules are set by each state. Check with your state regulator before you sell any tickets.
Not always. Permission to run a raffle doesn't automatically include online or cross-border sales, so confirm both with your regulator.
Before your first ticket sale, not just before the draw. Selling before your authorization is issued is the most common and most avoidable breach.