Most classes have at least a few skills that scale off of Focus and levels, but not weapon DPS. Berserker too. But I don't know if a Focus Berserker is viable, even if the magier skills have more range.
Wolfpack is the skill for focus zerkers. It's about as OP as Emberquake for engineers.
With Embermage, it isn't necessarily better to not use skills that scale off of weapon DPS. I think they still scale off of Focus as long as they're elemental, but those skills may still scale with Strength as well (but Strength would still not be useful).
I'm not sure which scalings add and which multiply, but there might not be much of a point in getting any Strength points at all on an Embermage.
Strength adds to weapon damage, and focus adds to all forms of magical damage. Strength also increases critical damage, which multiplies. Everything except damage over time can crit.
The question of how much Vitality you need depends on the difficulty level and how many NG+'s you have racked up, probably. Notice that Vitality scales up your flat damage reductions a bit, making it more useful than just having +Health gear.
Not even close. Armor ratings are worthless. More HP is always better. Vitality should only be used to meet equipment requirements and increase block chance if you use a shield.