I played THM in P3, so I can kinda talk from that side.
Sustainability is no problem for THM. Their key mechanic ensures this. When you cast Fire spells, you get an "Astral Fire" buff - boosts dmg, but also boosts MP cost, & stops MP regen. Casting Ice spells gives you the "Umbral Ice" buff - lowers dmg a little, but boosts MP regen massively. You also have an ability (Transpose) to swap your current buff for 1 stack of the other (can have 3 stacks later on). Essentially, you'll burn your MP with Fire spells, Transpose, toss out your Thunder DoT + Ice spells until MP is full (about 10 sec usually), transpose back & repeat.
In mass burn FATEs things don't live long enough to worry you. In single-target bosses, any tank on the scene should be able to hold off of you. Groups are the same for any DPS - given you can't choose your role for Duty Finder (you can heal lower-level dungeons pretty easily if you have Cure from a Conjurer). Soloing is not much of an issue - your firepower is top of the line. Again, grab Cure from Conjurer, and Protect is good too. Be aware that you wear cloth, and keep range. Blizzard I gives a heavy status (slow movement), Blizzard II has Bind (but is Point-Blank AoE, so use it & run!) and you have Sleep for hairy situations.