Skills

[Zakilevo]

I know they have a brief explanation in Wiki but I want to know if they influence additional things.

Swordfighting - Tournament, Duel, something to do with commanding infantry units?
Jousting - Tournament, something to do with cavalry units?
Leadership - Withdrawal %, Unlocks more advanced marshal settings.

[Nosferatus]

Yes that's right.
Leadership also gives better organization to your unit and will preform better in battle.

[Stue (DC)]

I believe that swordfighting likely helps in battle when you are commanding infantry troop, to give it some more effectivensee, while at the same time you can improve that skill by commanding infantry troop.

the same (likely) applies for justing.

these statements would need more confirmation from those who know. it is certain that you for can improve your justing/sfighting/leadership by using adequate troop in battles, but i would like to hear more confirmation that infantry troop commanded by good swordfighter is somewhat more effective.

swordfighting also helps against infil attacks.

leadership of marshal should also improve army troops org in battle, while that parameter was always mistery to me and it seems that it disappeared from current troop reports.

[Bedwyr]

Here's what I know...

Swordfighting: Helps in duels, helps in tournaments, helps in defending against and in making infiltrator attacks, goes up in battle sometimes if you command infantry units, don't know if it influences the battle but I wouldn't be surprised.

Jousting: Helps in tournaments, goes up if you command cav in battle, may influence battle.

Leadership: Withdrawal %, marshal settings, has some effect on how your unit performs (even beyond withdrawal settings).  I have heard rumours of other effects at high leadership.