Where does Congress get authority to call people to testify? Doesn't this undermine the Judicial branch?

I find these depositions in front of Congress, i.e. "Spygate", confusing. Isn't this something that should be taking place in a courtroom, in front of a judge, under the judicial process? Congresspeople do not necessarily have backgrounds as lawyers or judges. Are those testifying before Congress always granted immunity from incriminating themselves (short of lying)?