Awkward phrasing in English. I can see "This is the train here" (we were waiting for a specific train, and it has arrived). But "This train is here" seems odd to say and unlikely to use in common speech.
Yes, it is. With ez/az/ezek/azok (this/that/these/those), you have to insert the definite article. And both "ez" and "vonat" get conjugated, if conjugation happens.
I agree with TonyWare1 and GrubbaFong about how this sentence would be naturally spoken in English (English is my native language). In English, you would almost never say "This train is here". The word "This" sounds very unnaturally awkward in that English statement. It would be more common to be saying something like...The train is here, your train is here, our train is here, a train is here. - "This train..." sounds like bad English, unless you were doing something like...pointing to a picture of a train. Even then, you would say "That train is here".