Can you just go sit in a court and observe a Judge in action.?

Question

In family court?or civil court ?

Answer 1

yes

Answer 2

It may depend on the laws of your state but generally you can go watch criminal and civil hearings/trials (in magistrate, state or superior courts, including state appeallate courts) unless the judge has specifically closed off the courtroom to the public (which is very rare).

Juvenile proceedings are generally closed to the public to protect the minor.

I beleive federal trials run along those same lines (of course, I'm pretty sure there is no federal counterpart to juv court).