No, a man wearing a kilt is not wearing a skirt. Some men will loudly say so, because, after all, to accuse another man of being feminine is a horrible insult. But these jokers are both culturally dyslexic and jealous. Women flock to the male of the Scottish species in his colorful plumage.

Yes, traditionally the kilted Scot wore no undergarments. “Going commando” is what it’s called today. No, it’s not required.
The original Highlander started out with a knee-length shirt, then wound yard after yard of wool cloth around his body and draped the end over his shoulder. Since he spent days clambering up and down icy rock- and heather-strewn slopes, it was helpful having clothing, blanket, and pup-tent in one package.
The bulkiness of the “great kilt” was why Scots warriors would wear only their shirts when charging down on an enemy. They didn’t paint themselves blue, although all those newt-like complexions no doubt turned blue from the cold.