What if Meade had let Burnside stick with his original plan of sending in the trained colored troops first at the Battle of the Crater? Would it have turned the battle to a Union Victory;
Probably yes. Though Ferrero, commander of the USCT division, was apparently no better than Ledlie, the gross incompetent of the division that was sent in first. But if the USCT go in first, and their planning was at all useful, I think that momentum would carry the Union attack clear through the Rebel line.
It's possible that even so, Lee would have contained the attack at some point, but it seems likely that the entire line to the west would be forced back, cutting the South Side Railroad, and forcing the Rebels out of Petersburg.
would Petersburg, and thus the Confederacy, have fallen earlier?
Petersburg falls. It's generally conceded this means the fall of Richmond, though I'm not absolutely sure why. (The primary rail connection from Richmond to the Deep South ran through Petersburg - but it was cut when Petersburg was besieged. There was a secondary line from Petersburg to the west and southwest - but it intersected a line running directly SW from Richmond, so I don't see why it was vital.)
If Richmond goes, the CSA takes a big hit and probably dies by the end of 1864.
What are the effects? On reputations (of Burnside,
A significant boost. He might end up as President. OTL, he was remarkably popular despite Fredericksburg and the Crater. Most of the other generals liked him, and he had enough fans in the rank and file to be a Commander-in-Chief of the GAR and the first head of the National Rifle Association.
I think it gets the USCT a good deal of credit.
On Lincoln's re-election?
It becomes a lock.
I can't see a
direct effect. There would be substantial effects from the earlier Union victory, and butterflies galore, especially regarding Lincoln.
The higher profile of the USCT could lead to earlier support for black suffrage.
On anything else I'm not thinking of?
Possibly an improved reputation for Meade, though I don't know how much the Crater fiasco was attributed to him at the time. Also perhaps a diminished reputation for Phil Sheridan - no Valley Campaign, Five Forks, or Appomattox. Some other battles (in North Carolina?) might replace these.