When we say this sentence, is it compulsory to use "around"?
It's not compulsory, but it's more natural.
Is it unnatural to say "he kids with everyone"?
I think we've already establish that it isn't very natural.
One natural version you will hear is "He's kidding (around)". Here, 'around' is optional. However, if I were to make this an imperative, and say "Quit kidding around", I would have to include 'around'.
When somebody says something you suspect may not be serious, you can say any of the following:
You're kidding (me).
Are you kidding (me)?
You've got to be kidding (me). (often used to express disbelief, particularly at something absurd)