Yes. For a direct object "the..." with an an adjective. The adjective requires a ה prefix. In this case, if there wasn't an adjective, and only במסעדה , then you can only tell by listening (ba or be) or having the nikkud dots.
That is just poor English. A restaurant cannot be emotional. Serious here can only be used as a descriptor such as 'a seriously good' restaurant or 'a seriously expensive restaurant'. Duo, please consult with native English speakers