Girlfriends should always be told that they are right ;) Apart from this fact, "Ez az a(z)" is how I've been thought to say "this is". But maybe "ez a(z)" is enough to express the same?

"van" is generally omitted and implied in Hungarian unless it's emphasized.

van is only used for is when specifying location.

My Hungarian teacher explained that "van" is omitted for the third person singular and plural. Except when asking a question with Hol or with Hogy, as well as in the corresponding answers: "Hol van Péter? Ő itt van."