Question-—Is Trump a private citizen or is he still the President?
And that's just it.
Under what authority can the Senate hold a trial and potentially convict a private citizen?
He’s a private citizen and cannot be removed from office. The Constitution is very clear on Impeachment:
The Senate shall have the sole Power to try all Impeachments. When sitting for that Purpose, they shall be on Oath or Affirmation. When the President of the United States is tried, the Chief Justice shall preside: And no Person shall be convicted without the Concurrence of two thirds of the Members present.
Judgment in Cases of Impeachment shall not extend further than to removal from Office, and disqualification to hold and enjoy any Office of honor, Trust or Profit under the United States: but the Party convicted shall nevertheless be liable and subject to Indictment, Trial, Judgment and Punishment, according to Law.
———-
The disqualification clause is directly tied to removal. Any pubie who votes for this will be primaried.