is that the Chief Justice presides over the trial in the Senate. That's it. The SCOTUS has no investigative powers.
We've had one presidential impeachment tried in the Senate in recent history. One, and that's it. That's the only model we have to look at. Clinton was not removed from office by the Senate. In fact, NO PRESIDENT HAS EVER BEEN REMOVED FROM OFFICE by the Senate.
Nixon didn't even have an impeachment in the House. He resigned before that could occur.
The Senate proceedings in the Clinton case were handled a lot like a trial. I'd have to go back and review what happened exactly, since I can't remember the details now.
House impeachment proceedings involve investigations and committee hearings. That's a different process altogether. The Senate serves a a jury in the second phase. a 2/3 vote is require to remove an official from office. That makes it almost impossible if the Senate has a majority of the same party as the President. That's especially true with Trump. There is zero chance of removal at this time. Only if Trump does something outrageous enough to piss off a lot of Republican Senators could he be removed, and that seems unlikely.
Taken in whole, if an impeachment proceeding started today, it would still be going on in 2020. That would seriously affect our presidential election process, probably to the extent that it would throw the whole thing into unknown territory. That's why there's not going to be any impeachment in the House, nor a trial in the Senate. There's an election involved.