lát - to see (to perceive with the eyes)
I think you mean this,
jár - to go out with somebody, to date (-val/-vel)(girlfriend and boyfriend)... e.g. "Járok valakivel - I'm dating someone"
Then there is also, randevúzik -(intransitive) to date, to take someone out on a date (someone -val/-vel)... e.g. "Randevúzol valakivel? - Are you dating anyone"
Yes: "Are you going out with someone", "are you dating someone", and "are you seeing something" all mean the same thing, at least in American English. "Are you dating someone" refers to a long-standing thing (or a habitual action), and is different from "Are you going on a date with someone".
I take it that "Te látsz egy rendezőt" is completely unrelated :-).