My theoretical Wizard has an aspect that has to do anger. Specifically "Fiery Temper." I'm trying to find a way to invoke that for bonus for fire spells. Would that be acceptable by general rules?
The main limit of what aspects can be used for what actions is basically what the table will accept - your GM and your fellow players.
My rule of thumb is, if I can say it in a sentence with a straight face, it works. I.E. "Because Chivalry's Not Dead Dammit, I hit the demon that's attacking my girlfriend really hard." So lets try that. "Because of my Fiery Temper, I keep good control of my fire spell." That doesn't sound right to me. "Cold Fury" might do, a kind of clarity that comes from anger. However, there are two parts to spellcasting, power and control. "Because of my Fiery Temper, I pump extra power into my fire spell." That does make sense to me, so if I was another player at your table, I'd accept that aspect being used to boost power, but not rolls to control.
The other players might see things differently! Asking your group or the GM if a general kind of action is an acceptable target of an aspect is perfectly fine during character creation, especially if it's something you plan to do regularly. If you wanted to be sure, retooling the aspect to be a little more evocative or specific might be advised; That aspect looks a little bland to me. For example, "Pyromancer's Temper" might let you use it both on control and power rolls, while still getting you the same idea since it's a bit more specific. "I solve everything with fire" is might be more than you wanted, but it certainly will let you use it for fire spells!
Also keep in mind that to be a wizard, you have to have an aspect that makes that clear. (Same for every template really.) You can pretty much always use that to boost your spells. (I think they even mention that specifically in the rulebook.)
Yes, that's totally legit.
So long as you can describe how your character's aspect is beneficial to the circumstance of the roll, you can spend the Fate point. The GM (and the rest of the group) may ask for more clarification if they're unsure how you're justifying the use, though. Sometimes it'll turn out they think it's too much of a stretch and the GM will hand back your Fate point, so be thoughtful about your invokes.
Since this is a core concept for your character idea, you should probably talk with the group during character creation about how your wizard's Fiery temper fuels his spellcasting so it's not a surprise to anyone when you bring it up mid-combat ('cause stopping to explain it then would slow things down a lot)--and so you know if there's a limit on the kind of bonus to fire the group will consider reasonable coming from a temper-based aspect. Examples of rage-fuelled fire powers from media (like Zuko in Avatar: The Last Airbender) could help explain your idea.