[FreeReign]

Sure, they could have their hearings and trials but they have no clear constitutional authority to rule in this matter.

Election fraud? They have no Constitutional powers to rule on that?

Sure they do.

They could invalidate fraudulent election results and they could invalidate any certifications and any slate of electors based on those fraudulent results.

[Mariner]

No seated federal officer has been removed by a court for any reason, including election fraud.

Once seated, expulsion (congress) or impeachment are the only mechanisms.