If a member of Congress (e.g. Representative Schiff) subpoenas phone records of people (which is allowed) and releases them directly (in a report) or indirectly (leaked to press). Does this violate any (e.g. privacy) US Laws? Or, if there is law for a court subpoena to keep records private (e.g. a Grand Jury), did/could Congress exempt itself from these laws?
The power to issue subpoenas is created by rule, so while an individual Congressman cannot currently issue a subpoena (instead a committee does), the rule can be changed. So it would be possible for a Congressman to issue a subpoena. He could release information obtained via the subpoena, and is immunized from legal repercussions by the Speech and Debate Clause of the Constitution. However, there is no immunity against action by Congress, so he could be disciplined under House or Senate rules. Disclosure might be a violation of House rule VII 3.(b)(2), or committee rules established under Rule X(11)(f) or XI 3.(a)(4), or other House rules or committee rules, which can be modified by majority vote. The House has no power to imprison its members, but they can be censured, or expelled by vote of 2/3 of the members (Art. 1 sec 5 of the Constitution).
If the heart of your question is, under the current rules, has anything been done wrong, I would say no. Other than the special case of a grand jury, our system allows/requires public dissemination of information regarding prosecutions.
Another answer refers to House Rule VII 3.(b)(2) - it is
2) An investigative record that contains personal data relating to a specific living person (the disclosure of which would be an unwarranted invasion of personal privacy), an administrative record relating to personnel, or a record relating to a hearing that was closed under clause 2(g)(2) of rule XI shall be made available if it has been in existence for 50 years.
My reading of that is if the personal information is not made public as required by default in the immediately preceding section, it must be made available in 50 years. It does not require secrecy of anything for 50 years. It is rule about disclose, not a rule about not disclosing.