Invalidating an election
Diane Blumstein, Nancy Goodman, and Donna Soodalter-Toman argue in the case, that Russia cyber invaded America and that our Intelligence Community’s reports in October and January, along with the FBI’s public statements prove that our Executive Branch concluded a foreign invader influenced the 2016 elections.
The Occupy Democrats item noted that the referenced court action was “a longshot” and later indicated that the petition “has a 1% chance of even being heard by the court, let alone of being decided favorably” for the petitioners.
This case was notable because it established a new (and relevant) exception.
Typically, a court can only overturn an election when it's clear that some irregularities the election to be decided unfairly.
Elections are governed by laws, and it is the responsibility of the judicial branch to resolve disputes over laws.
Those laws could also be considered the doctrines to answer your third question.
That designator was widely interpreted as a tacit indication that the Court had decided the claim had merit and ought to be discussed, but consultancy firm Counsel Press noted in a 2012 blog post that “distributed for conference” is no specific barometer of a petition’s likelihood of being heard: Every petition that is docketed at the U. Supreme Court, and remains on the docket, will eventually be distributed for a conference, usually held on a Friday.After a challenge in the Alaskan Supreme court Nageak ended up the victor by 2 votes.For your second question, I don't know of any case where the courts ruled themselves unable to overturn election results due to separation of powers, but I don't think its very realistic to have such a case.Well into the latter part of 2017, social media users continued to circulate an image touting a petition seeking to overturn the results of the 2016 U. presidential election due to purported Russian interference, even though the information it referenced was long outdated. Our Supreme Court set the case for Conference on Friday, March 17th to put the petition in front of all of the Justices. There has never before been a case about the Constitution’s Guarantee Clause (which obliges the federal government to protect states from foreign invaders) like this decided in front of the Supreme Court.