But how would you cover using earthbending to toss together a building, reinforce a fortress wall, or what have you?
Hm...to me, this sounds like something that's more likely to be kind of a "preparing for battle" or "helping repair the city" challenge, yes? In that case, I'd lean towards not highlighting it with a particular ability but just defining it as an option for other abilities. Is the assumption that all your characters are benders of some kind or another? If so, here's an option:
At character creation, everyone picks a "bending" style. It isn't an ability, just a note on their character. Then, when they want to do something like the above tasks, you assign it a difficulty level and they can pick appropriate abilities to support it. For instance, to toss a building together it might help to be Smart or have Knowledge: Architecture. Maybe something like Knowledge: Siege Warfare might help reinforce a fortress wall. Other "bending" styles could have their own concepts too.
Alternatively, I could see creating a Unique Ability for each "bending" style that's usable for the non-combat applications of the ability. So you'd have, what, Earth-Bending, Fire-Bending, Water-Bending, and Air-Bending? That way a character could choose more than one--that was a thing on the show, correct? Then, anytime a character wanted to handle a non-combat challenge with the power, you could let them use that trait.
One further approach is that you could create the different "bending" style traits, but let them work as elementally-bound versions of Magic, Arcane (and remove Magic, Arcane from your game). Just use the rules for that, and limit it to effects reasonably linked to the element in question (which, to be fair, could be very widespread...there's a lot of things you can justify with any of the four elements). Then let it work for the more skill-challenge concepts as well.
Hmm. Alchemy has limits beyond "whatever you want to do" though; the characters are limited to transmuting the chemicals present in their current location. Characters in FMA typically have a reserve of tricks they commonly use in combat (only the main character and his brother really have the expertise to make up whatever effect they need on the fly)...
In that case, you might just have them have the different abilities instead of Magic, Arcane. If they're more limited than I thought, it seems like you can just kind of pick their "signature" abilities and away you go.
As far as the limitation of needing to transmute present materials...whether you want to represent that or not depends on how often it's actually a limitation. If they generally have something to transmute so it's more of a "once-in-a-season" thing that they don't have what they need, then I wouldn't put a Weakness or Flaw on there to represent it. Instead, I'd just create a situation every few plots where the characters didn't have materials they needed and hand the players some drama dice for going along with it. Rather than taking a weakness that won't come up much, they just get paid for you making it part of the plot and forcing them to work without character abilities they usually have.
If it comes up frequently, on the other hand, that sounds like maybe a simple variant on the Focus weakness (rather than requiring an item that you carry with you, it requires materials that are usually present wherever you are...same basic effect) or the Requirement flaw, depending on how you wanted to model it. Suppressed Power could be appropriate as an alternative as well.
Basically, put something on a character as a Weakness or Flaw if it's something that will matter reasonably frequently. If it's something that'll only come up every once in a long while, you may instead just want to establish it as a world rule and tell the players when it comes up they'll get some drama dice. Or, heck, if your players will accept it, just tell them it's a world rule and they don't get paid for it when it eventually comes up.

I prefer paying them, but I'm a pretty nice GM.
...but given a bit of time, they can accomplish basically any transmutation they would like.
If this is important to the story, it could be addressed with a variant on Inventor, perhaps (if Magic, Arcane didn't seem to be what you were going for). Just label it Alchemist instead, and I think it would pretty much work for what you're going for. Instead of creating gear, it creates lasting alchemy effects. Like Inventions, they can either be story effects/justifications for using your existing abilities or can actually be built from abilities and weaknesses like Gear could be.
Alternatively, just as with the "bending" concept, if this is just something that
all player characters can do, you might just make it something that's generally available in your game and not have an ability specific to it. Figuring out how to properly create an effect could just be an application of Smart and/or appropriate Knowledge skills, as one example. You don't necessarily need a special ability for it, if all characters are pretty much going to have that.
Can you explain what you mean here a bit more?
Basically, take "Flame Blast." Your idea of how a "flame blast" should work might differ from mine. Maybe you want it to be a low damage attack that sets things on fire to do continuing damage, while I picture it more as a high-damage vaporizing blast of heat that explodes to do area damage but costs me some Endurance. Under a system like this, whoever is making the character can make their own idea of "flame blast," instead of having to go with whatever the book's version is.