What was illegitimate about Colorado's electoral votes? The legislature was completely within its rights to choose electors.
It was certyainly legal, but still morally uncorrect to give Hayes 3 more EVs without any mandate from the people (of course, CO would have gone to Hayes anyways, but still).
Theorically, someone can win EVs with 1% of the vote (ridiculous turnout, structural luck, victory in small States, division of opponents).

Reallistically, the PV margin should be inferior to 3%.
Yeah. I noticed that the largest popular vote difference between the winner and the loser where the loser of the popular vote won the election was a 3% PV margin (Hayes' 48% to Tilden's 51%). That being said, I think a 5% margin could be realistic, since in 1948, had Dewey carried Ohio, Illinois, and California (all which were won within less than 1% of the vote), he would have won the election despite losing the popular vote by a 4.5 margin.
Yeah, you're right. Also think to 1916, when Hughes just needed California to win, despite Wilson would still win PV with 2,74 more points. 1948 is really a unique event in the history, considering that even in 1876, voter fraud, an uncorrect apportionment, and te Colorado's 3 unlegitimate EVs caused an extremely narrow Hayes victory.
Some of the voter fraud in 1876 favored Tilden, like in Mississippi.
It was irrelevant since he won 2-1. Frauds allowed Hayes to win in LA, SC and OR by extremely narrow margins.
Hayes definitely would have won MS had there not been a massive voter intimidation campaign against black voters, who were a substantial majority.