Hungarian is nothing if not inconsistent. :) If you want to learn how Hungarians use it, then this is how you should learn it. Or actually, both ways. And both ways should be accepted.

"vécéc" is not a Hungarian word :)

It's widely accepted in spoken Hungarian. Usually you need a verb when you have an adverb (& thus have a so-called nominal-verbal predicate), but in some cases it can be left out.

(If you want a parallel in English, think of all the times when English speakers drop pronouns: "Met him yesterday. Talks all kins of nonsense.")

No, that sentence needs a verb.

Toalettpapír, double-t, and one word. Might not be used too widely, though.