"What authority does POTUS have specifically over the Marines?" - #14 "Focus on the power of POTUS as it relates to the Marines." - #17 "Can the NG work in coordination w/ the marines? Do conditions need to be satisfied to authorize?" - #22
Code Federal Regulations - Title 32 National Defense - PART 631 - Subpart C: Off-Installation Operations (Military Patrols and Investigative Activities) and Policy These regulations deal with the military and how they assist with law enforcement. Some might say, BuT PosSe CoMiTatUs! Sure, let's look at 18 U.S. Code § 1385 - Use of Army and Air Force as posse comitatus. It's true that POTUS cannot use the Army or Air Force as posse comitatus without Congressional authorization.
HOWEVER, these restrictions do not apply to the usage of the Navy, and thus not to the usage of the Marines. Have a look at the Marine Corps Policy from the above CFR for details on how the Marines may be used "To assist Federal, State, and local law enforcement agencies within the limits imposed by higher authority and the Posse Comitatus Act," they remain "under the command of their Marine superiors when accompanying civilian police" and they "may come to the aid of civilian police in order to prevent the commission of a felony or injury to a civilian police officer." POTUS can use the Marines to help all non-military police forces to arrest traitors and insurrectionists and doesn't need any permission from Congress.
Yes, the Marines can work in coordination with the NG, and it's possible the NG has already been activated per the Insurrection Act. The conditions have been absolutely been met to justify POTUS using the NG and armed forces to enforce Federal authority. Granted, POTUS does not need any permission from Congress to use any regular military forces for defense against insurrection and rebellion. But those forces cannot be used to make arrests unless authorized by Congress. However, the Marines can make arrests under the authority of POTUS, without being barred by the Posse Comitatus Act. Arrests are the important aspect of this whole thing. Could regular civilian police make such a massive amount of arrests on their own? Are they reliable? Marines seem to be the better option, at least as support.
"What former President used the military to save the republic and what occurred exactly?" - #22
Washington used the military to put down the Whiskey Rebellion, but the more obvious answer would be Lincoln. Without his willingness to use the military to preserve the Union, the Republic may well have been forever sundered as a result of the Rebellion in 1860-1865. What happened? Rogue state officials (governors) and federal officials (Congressmen, judges etc) engaged in organized, mass insurrection and rebellion under illegitimate state "governments" to disregard the authority of the federal government. Sounds a bit similar to what occurred with the recent "elections" in certain states....
Fun fact : The Marines are older than America
Nov 10, 1775. Tun Tavern.
Older than the Navy too, by a bit.
Thank God for John Adams! (Aside from Lincoln, he's my next favorite mostly because he is the least appreciated and often misunderstood President)