"He must enter a café."
Translation:Il faut qu'il entre dans un café.
My understanding is that il faut is always followed by que because it means "it's important that" or "it must be that" then followed by the thing that must happen. The "il" is an abstract "it", and doesn't mean the guy going into the cafe, and "que" means "that". It'd be "il faut qu'elle..." if it was about a woman.
No, it isn't always followed by que - for example:
Il faut se dire au revoir, le train va partir.
"We have to say goodbye; the train is about to leave."
When it is written as above - "il faut que + [sujunctive]" - it means "it is imperative that" / "it is necessary that", as you indicated in your post.
You could probably avoid the subjunctive altogether by saying "Il doit entre dans un café" as the conjugation of "entrer" in the third person singular is identical in both the indicative and the subjunctive.
Having said that, I have no idea whether that would be accepted, especially if this sentence belongs to the subjunctive present lesson group.
Yes. The verb "entrer " is, for the most part, an intransitive verb and cannot take a direct object. It is regularly used with a preposition, especially "dans" when the meaning is "to go/come/get into".
It is can be used in a transitive sense when referring to computer input:
"Veuillez entrer votre mot de passe " → "Please enter your password"