Fighters are the generic warrior who lives and fights by his own expertise. Their combat abilities are just that and should be learned in the heat of battle. Yes, they could practice tactics such as disarming outside of combat, but the same could be said of any combat related skill. Thus, they should all remain within the domain of c.
There are some skills that any adventurer should be able to pick up over time. Things like repairing a weapon, skinning a corpse, or finding nature resources are things fighters should be able to do, which are not combat related. Actually, ANY guild should be able to do these things in theory. The world lore skills are already set up this way.
The Spec category should be reserved for those whose primary profession is some specialized craft. Fighters' primary focus is not a craft, but fighting, so realistically, they shouldn't even have a Spec category of xp. This was the case in early cms, actually. Whether this is feasible or balanced is another matter (although the issue of overall levels is easy to fix, as are most of the typical rebuttals to this).

On the subject of armour: I am strongly opposed to anything that limits the armour a character can wear based on class or training. Any strong person can put on a suit of armour, which will protect them even if they just stand there. (the ability to dodge blows is covered by the dodge skill) The urge to limit armour is usually a result game balance - but there are other ways to encourage "squishies" to not wear armour, such as making spellcasting in armour more difficult or fumble-prone.

You also hint that spellcasting and lock picking might be possible, but difficult, for fighters. I advise against going down any path such as this without serious and lengthy design meetings as it completely changes the nature of darke. To be able to cross-train skills was one thing that was added (more or less) in pre-cms darke but quickly realized to be rich in balance problems and abuse issues, and removed. Such a change would require an extensive redesign of darke and shouldn't be considered as a balance tweak.