What is more correct and why? I heard few British people speaking "in slang" and some of them said that unofficial language is named "slang."
Additionally, is "slang" official/polite word?
Slang is a type of language rather than a language in itself, so one would ideally say that someone was using slang. 'Speaking in slang' is not really correct. 'Is it slang?' would be better, but to play it safe you might say 'is it an example of slang?'
A closely related term is the noun 'colloquialism', the adjectival form being colloquial. You would say:
Addendum: as colloquial language generally comprises relaxed grammar rather than a set of informal words, the terms are not necessarily interchangeable--as kiamlaluno rightly pointed out below.