Targeting is solely for user-input - it has nothing to do with output. Ask the question: what does the player have to do to cast this ability? Where does the cursor have to be?
Area of effect is a damage classification. Both "spelleffects" and "damagetype" are used for damage classification - and you've been adding spellaoe already. "spelleffects" is perhaps a poor choice of name for the parameter given it's used for non-spells, too, but "damagetype" is already taken.
"Area of effect" and "spellaoe" can be used interchangeably. I intend to merge/delete the old damage type templates (e.g. area of effect and single target) with the new ones (e.g. area damage and spell damage) - I just created new ones to make transitioning easier. Those two examples are ultimately the same thing - you'll notice the information is the same.
Regarding Brand's innate - spelleffects and damagetype both accept "Special" which says "See notes", and you should describe the multiple classifications in the ability details. The input is passive - the ability triggers itself. The damage over time is Persistent damage and explosion is Area damage.
Pretty certain the dot damage type is only dealt by things that are actually applied to the target, like a bleed or poison (so aoedot would be Singes's Poison Trail). The damage type doesn't always match the ability - Senna and Jhin have a lot of single-target damage considering they have aoe spells. I can check the API for Fiddle specifically when I get home, or you can ping Frank on Discord. I could just be misremembering. You can put it as aoedot for now if you want.
However, while discussing this with Frank (our resident game-file diver), it became apparent that we're still not accurately documenting damagetypes.
There's the original engine-level damage type system and a relatively new script-level damage type system. Crowstorm deals spellaoe on an engine-level. Spellvamp, Gunblade, etc, interacts with engine-level damage types, which is why Crowstorm heals for one-third effectiveness.
However, Riot added a script-level system that interacts with runes and other more modern effects. Possible tags include: aoe, periodic, indirect, basicattack, activepsell, proc, pet and nonredirectable. Crowstorm has at least aoe and period (didn't ask for the full list). An effect like Arcane Comet just has a priority system - so abilities with both aoe and periodic will prioritize the periodic behavior.
Both the engine-level and script-tags are to be assigned arbitrarily by a Riot engineer and there's no guarantee they will match. There could be a engine-level single target ability with the aoe script-tag. We can hope that our current spelleffects options cover all possible outcomes - but in the future it might ultimately be necessary to have separate |enginedamage= and |scripttags= in the future.
However, this shouldn't affect the current project. Currently, 'aoedot' is the only non-engine type supported by "spelleffects". So if we do need to update it in the future, spelleffects is already the same as enginedamage except for abilities with the aoedot type - so updating that short list shouldn't be too hard.