The Mage does not have a spell list - it was created explicitly to get away from the silly idea that you need a list of spells to do magic. With The Mage, you make up what you want your spell to accomplish on the fly, and depending on how well you roll determines what sort of limits the spell has. The spell will always have consequences, even on a 10+, because making up any sort of magic effect you want is a very powerful ability.
A 9th level Mage doesn't explicitly cast spells better than a 1st level one, that's not the point of Dungeon World. Dungeon World has a very flat leveling curve, which is one of the best things about it - don't relegate Mage spells to any kind of 'level' thought process. A 1st level Mage of The Dragon can burn down a city almost as well as a 9th level one, but the 9th level one will probably have some advances to make it go smoother and burnier.
The Focus benefit used to be a straight +1 to your Aligned spells, but this was essentially too good. However, having no benefit at all didn't make much sense either. So instead, it is a reasonable bonus that mostly helps in three situations: When The Mage is laden with INT penalties, when The Mage has -forward penalties he wants to ignore, or when someone with crappy INT multiclasses into Mage and still wants to spellcast. It ensures that at least your Aligned spells will usually work well.
Yes, the Mage rolls their class damage when dealing damage with their spells. It's the entire reason they have a d8 in damage.
I hope that helps!