Yes, characters can freely switch between weapon sets. And shields also apply AC even if they're not currently equipped weapon set.
It's not a bug in itself, but rather a convenience feature as it would only add trivial tediousness and annoying micro-management by having to pay constant attention to what the party members are holding in their hands.
As for the shield thing... the game does not visually show other weapon sets equipped, but in reality the shield would be hanging from the back and as such offer protection even if not equipped. So it makes sense to provide protection even if not currently held.
If the game still had backstabs as it previously did, then they could have made the shield protect you from the back when not held in hand and protect you from the front when held. But they removed backstabs, so it just applies general protection.
