I just see your question , but astonishingly find: you are from USA, you should have been very good at English with English your native language. Such question should be asked by non English speaker (for one thing, a Chinese like me) rather than YOU, but in reality, you are indeed a native English speaker , which is evidenced via your profile, so I badly imagine that you are not from USA but you 'd like to be so. By the way, all persons who answer your question are all not native speakers including me(lol). Sorry for my absent reply.

Yes

Exactly! It means they came to eat lunch.

Yes, you're right!