the alerts/schedule system seems redundant, but in fact allows for a high degree of pre-sets and customization. Each alert has a schedule for active squads, and a set of burrows to restrict civilians to. By hitting enter on the left column for alerts, you set the civilian population to the burrows allowed in that alert. Or, you can ignore that, leave civ on inactive all the time, and just select which burrows you want when a siege/ambush happens, and manually deselect the burrows to remove restrictions when the siege ends. Then, squads can be set to different alerts individually, this is done by highlighting the alert, moving over to the middle column, and then hitting enter on the squad. At that point each squad will do whatever is described in the schedule for that squad under that alert.
Even without setting the squads to active/train they should have picked up equipment and done individual training drills when not busy with other jobs.
The job title reflects a dwarf's highest weapon skill, not the weapon currently assigned. A dwarf gets this job title when he is under alert that has a specific order (or a station/kill command). Dwarves are not considered on-duty if they are training in a barracks while no orders are assigned. They will only do individual combat drills in this circumstance, they will keep their civilian profession name.
happiness dropping to 0 because of training is caused by 2 things. There is a bad thought associated with "the draft" when a dwarf becomes set to an alert that gives him any order when he doesn't have any military weapon skills at novice or better. You can tell because his job will be "recruit." At one point, going on and off duty multiple times could cause this thought to stack rapidly with itself, which was bad. Not sure if that's still the case. The second bad thought is "grumbling/depressed/enraged by long patrol duty." This is caused by many months of consecutive active duty. These thoughts are often ignored by players as they aren't that serious if the dwarf has nice things to admire kill, and they stop getting this thought when they become champions. If you don't want to see these thoughts, they can be countered by giving dwarves months off. Or setting minimum number in the shedule below the squads full size, which allows a few dwarves to do jobs and be civilians while others in the squad are training. Not many people bother with this second option though.
As for overall training strategy, smaller squads lead to more sparring and thus faster skill gain. Dwarves will not spar until they all have a couple levels in their weapon skill. Demonstrations teach skill very slowly when the guy giving the demonstration has no teacher skill and only novice in the skill he is teaching. 2-man squads have been proven to churn out legendaries faster than any other training strategy save danger-rooms or perhaps training weapons vs chained/live targets.
If this helps, I never set up uniforms - I equip every single dwarf manually.
As in, go to equip, and select their gear dwarf by dwarf.
So far, it has worked perfectly! My most recent dwarves dutifully picked up their bucklers, crossbows and shell/leather armor, and went to practice at the archery range.
manually equipping lets you pick specific items, but those items aren't removed from the list when equipping the next dwarf, which i believe causes issues (have to use selective forbidding for this).
I find uniforms save time, especially if you move dwarves between squads.