No, var is the imperative form of the verb, which is the normal way of expressing commands & requests in Swedish.

That is the infinitive form, and in that case you place Inte before. "inte vara blyg" = "to not be shy".

It's the imperative of vara, 'be'.

I tried that just for fun, but I knew it wouldn't be accepted. I would really only use it in a poem or a song. If you wrote it in an essay (for whatever reason) the marker would probably cross it out and write "Don't be shy."