Combat demonstrations will occur, when one of the dwarves in the squad that's training has better skills then other dwarves in his squad.
Demonstrations become more effective, when the demonstrating dwarf improves teaching and leadership skills, and the observing dwarves get better student/concentration/observer(?) skills
I think sparring does not occur until the dwarves have at least some fighting/dodging skills.
Someone gave me the hint to make squads of 3 dwarves (it helps to make have dwarves in a squad use the same weapon), to increase the chance of them sparring. It seems to work.
I got 4 squads of 3 dwarves now. They alternate sparring and demonstrations fine. I assigned each of them a seperate barracks, made of a single weapon rack. The weapon rack only allows training, for the appropriate squad. No individual, or squad storage, or sleeping. (Why would a dwarf ever need to drop his weapon/armor anyways?)
I do *not* build any armor stands in the barracks. I've found that they're bugged, at least in respect to carried food. Dwarves will drop their carried food at the armor stand for some reason, where it rots. Annoying part is, nobody can haul away the rotting food, because it still is owned by the dwarf who put it there. With no armor stands, carrying 3 food works fine (provided they have backpacks).
When setting schedules, notice that you can edit the minimum number of dwarves required. The usefulness still puzzles me though.
I've tried alternating 1 and 3 dwarves minimum each month. Indeed, when a minimum of 1 is set, only 1 dwarf will train (individual combat drill), and the other 2 will return to their civilian jobs. However, all dwarves still get the 'grumbling/angered/depressed/enraged at long patrol duty' thought, even though they alternate between 1 month duty and 1 month freetime.
Same story when, instead of fiddling with the minimum number of dwarves, I tried alternating between 'Train' and 'no orders' commands.
They still get the same unhappy thought.
I have quite a hard time, keeping my military happy, at least until I get legendary brewers/cooks and a mist generator running.
Dwarves who are on 'no orders' revert to civilian status as well. Main difference with specifying a minimum number, would be that dwarves that have 'no orders' will still tend to go to the barracks, for individual combat drills, instead of doing civilan jobs.
EDIT: as for equipment, note that you can layer chain mail with breastplate. Greaves do not go over chain leggings though. Haven't tried leather leggings.