Dress specific dwarves in specific clothing

Dwarves will generally sleep wherever they see fit unless they have an assigned bed, in which case they will prefer this one. Sleeping in an assigned bed does give happy thoughts, being unable to makes a dwarf unhappy.

However, you don't generally have to bother with assigning beds since dwarves will claim unassigned bedrooms for themselves automatically.

Just a side-note: married dwarves and children share beds.

I can't answer your first question confidently, but I do have a few suggestions. This might be a stupid question, but -- do you have enough armor for them to wear as a uniform in the first place? Uniforms are often worn over clothing anyway (that might even be the default), are you sure they're simply not wearing their uniforms over their civilian clothes? (Scroll to the end of their inventory to find their armor and weapons, usually).

Your second question is easier to answer: Dwarves in your militia will, when they would otherwise idle, may instead go to their barracks and perform indiv. combat drills, even when inactive. This isn't nearly as good as active training (especially since indiv. combat drills never involves sparring), but it is usually preferable to your dwarves lounging about, socializing, and making friends.