I need help from British native speakers, but I think "knickers" means, specifically, women's underpants. OxfordDictionaries says "British: A woman's or girl's undergarment, covering the body from the waist or hips to the top of the thighs and having two holes for the legs." American Heritage says "a. Long bloomers formerly worn as underwear by women and girls. b. Chiefly British: Panties." Whether that means it is used more toward women or toward men, I don't know. I'll stop there, since Su.Ki. says other parts of my comment were mistaken.

It can work for guys, you can often encounter occasions in fiction/stand-up where something close to it (panties in a bunch) is used with the added insult of undermining a man's masculinity, implying that his concerns/worries/taking offence is more suited to a (stereotyped) woman than the true (toxicly masculine) man he should aspire to be.

You can use it for men/boys or women/girls. It ususally implies that the speaker thinks that the person concerned has over-reacted to something.

Hmmm, a great question. I would think that there is a definite answer to this question based on statistical study of a body of published texts, but my initial intuition is that this expression would not be the first I would think of when describing women. There is a similar expression using "panties" or "women's underwear", but the expression is somewhat vulgar, so I would not recommend using it. Instead, I immediately thought of the expression, "she was mad as a hornet". While this expression could be applied to men as well, I often hear it being said of women by men.

Yes, indistinctly. But implies that the person with their knickers in a twist is more agitated that the situation warrants.