2. (a) That's right. In cases of an undisclosed principal, provided that the agent acted within their actual authority when contracting, and provided that the agent intended to act on behalf of the principal, then the principal is entitled to enforce the contract against the third party.
It is somewhat difficult to justify this rule in terms of legal theory. It appears, initially at least, to contradict the doctrine of privity of contract. But the courts have made it clear that this is a commercially convenient rule and it is clearly established.