"We are going to a restaurant to eat dinner."
Translation:Ni iras al restoracio por vespermanĝi.
"Vespermanĝo" is the noun "dinner" (or supper, depending on where you are). "Vespermanĝi" is the verb "to eat dinner".
If we said "Ni iras al restoracio por vespermanĝo.", it would instead mean "We are going to a restaurant in order to dinner." In this case, we want the verb form for eating dinner, "vespermanĝi".
The infinitive is used to talk about actions in general. The -as, -is -os forms are used when you're saying who is doing them. So "ni iras" says that WE are going. But when we get to the part about "to eat dinner" we're talking about eating as a general activity. We are going for eating. Not "we are going for we eating."
That depends on where you are. Where I am, "vespermanĝo" means "dinner" and "tagmanĝo" means "lunch".
Literally, vespermanĝo means "evening meal" and tagmanĝo means "day meal". Whatever those may be called in your area.
PMEG says that "por" is needed to express intention. He doesn't include it in the PMEG, but you will catch Bertilo (the author of the PMEG) also using the "in order to" test described elsewhere in this thread. Note that there are sentences where this test will mislead you (Bertilo's example is "mi havas taskon por fari") but if you can say "in order to" then you do need "por."