What is the Federal Law regarding the protection of Classified Information?

There are several laws regarding classified information but as to marking classified information, the current standard is based on E.O. 13526: https://www.whitehouse.gov/the-press-office/executive-order-classified-national-security-information (section 1.6 for the markings section).
More of the regulations are found in 32 CFR Part 2001: https://www.law.cornell.edu/cfr/text/32/part-2001.

See https://www.archives.gov/isoo/training/marking-booklet.pdf and https://www.ncsc.gov/training/WBT/docs/CM_AltText_021312.pdf for practical classified marking methods. That's the basic guidance to mark classified materials. Some classified materials will have additional requirements that get added to the materials. And each department (State, Defense, etc.) has their own additional requirements and regulations.

Those entrusted with a security clearance and access to classified materials are also taught how to recognize classified (or potentially classified) materials even without the proper markings. If such information is found outside of proper channels or facilities, the information must be secured (if possible) and reported to a security official immediately.

For the 2nd part of your question, you'll need to review 18 USC 37: https://www.law.cornell.edu/uscode/text/18/part-I/chapter-37 sections 793 and 798.

If any mere mortal (typical workers with classified access, not the elite or political classes) were to have done anything remotely similar to what HRC (or even Gen Patraeus) did, they'd have their clearance/access revoked, be arrested immediately, and jailed while security officials investigated what happened. Only after the investigation is complete would they either be released as innocent or charged with a violation. If found to have been involved in a security incident, most have their security clearance revoked for a long time if not permanently whether or not another additional fines or punishment is levied.

The fact that members of the political or elite classes routinely flaunt the law or only receive a verbal warning or a slap on the wrist infuriates those not privileged with their status. This double-standard should not exist if the law was applied evenly to all citizens.

For digital classified documents you must use a computer with secured line that is approved of the corresponding clearance level. For physical documents or items they must be sealed and marked in the correct identifying marks of the classification level and handled by an assigned courier of equal clearance level after signing that they have possession of the documents. Spillage happens primarily with digital records than physical, as a messenger is still the most secure line of transport and communication. The burden of proof relies on whether or not those responsible for the loss of the documents is that of the security management team. If they are doing their jobs, there will be no issues. If not, then it is a failure on both parties and both are subject to judiciary punishment.

Oooh.... Rabbit hole...

Classified Information gets "tricky" because MOST of it is not actually covered under LAW, but Executive Order (WHICH IS NOT LAW). It has the Full Force of Law, in the Absence of Law, and Clarifies Existing Law.

Think of it like Military Regulations. You break one, you're screwed, but you didn't break a Law.

That's really a semantics issue, but it changes how things are (potentially) handled. E.O.s are subject to the whim of the Executive, whereas Law in theory applies to everyone.

Remember there are "rules" regarding the disclosure of classified information (we signed Non-disclosure agreements. VOLUNTARILY) However, some positions, by virtue of position alone are granted clearance regardless of who the person is, are granted a clearance. Specifically elected officials, and Senate confirmed ones. They don't go through the "standard background check" like the rest of us. You can't tell the President he doesn't get a TS President's Eyes Only.

For someone like the Sec State, who likely violated an Administrative Rule/Regulation/E.O. it boils down to the following:

1) Did she "knowingly" disseminate classified? That's knowingly is the biggest hurdle for CRIMINAL charges. Chances are the FBI has her dead to rights on NEGLIGENT. But going from Negligent to Criminal is the issue.

2) Did the leaks cause ACTUAL harm to U.S. interest. Actual vs. Potential is another huge hurdle. It also ties into the Negligence vs. Criminal aspect.

3) Context. All this went down at the same time as Snowden & Manning. Her "errors" (best neutral word I can think of) pale in comparison to theirs.

This is before we get into what is and what is not classified based on markings, and analysis etc. Guys like SSG James J. Palmer IV aka "JP4" and myself can't comment on news stories because "that's classified" even though their sources are 100% unclassified. It's not the information itself that is the issue, it's everything behind. It's like an Iceberg, the 90% you don't see is the problem. We may "know" something is classified, but we don't know how they got that information (in an unclassified way) which creates conflicts in marking.

A similar concept is "parallel investigations/construction" (where law enforcement construct a case using two sets of sources). This creates massive DOUBT when it comes to criminal intent. Makes it hard to press charges against HRC.