The Constitution says the chief justice shall preside. He isn't. That makes this trial unconstitutional, along with the fact that Congress can't impeach a private citizen.
That is arguable.
The COTUS says, in Article I Section 3:
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.
Since Trump is not president, that's how they are getting away with having a Dem preside.
I think the intent of A1S3C6 is that the chief justice, who is intended to be impartial, shall preside over such political trials, so I do agree with you about that.
Justice Roberts wanted nothing to do with this political theater, and that's why he declined. It does seem to send a message that it is unconstitutional or similarly flawed, otherwise, it would be his job to preside, and he should dutifully accept the obligation.
Regarding trying a private citizen, I think a president can be impeached after serving, because it simply makes sense. If you think about it, if a president did something really terrible, like sell secrets to China so his son could buy crack and is resulted in many US servicemen dying, I would want that POTUS impeached. Otherwise, the POTUS could simply resign and then run for another office. Or if it happened near the end of his term and was not discovered until later, he would be immune. That doesn't make sense.
constitution.congress.gov
Regards,
Jim