Yes, Virus is nice on dungeon bosses, and Eye for an Eye is also good from Arcanists. Do remember, though, that you can't use Aero as a Black Mage. Aero 2 is not cross-classable.

It depends on your gear and what level mobs you're killing if the dots are worth your time, but you could try throwing Thunder and Aero first and following that with Fire. Transpose to Umbral after mob is dead, run to the next one, and repeat. For dungeons, you can throw your dots first on trash and continuing normally from there. There are some trash mobs that have such a low HP that you don't get the full damage of dots, so you're better off just using Fire on those. As for bosses, start with dots first, and only refresh them only in Umbral Ice. Use Thundercloud proc when you can, but don't interrupt your current cast for it.

Stuff about BLM having all elements
Fire, Ice, Lightning trio is the classic Black Magic with a couple of status effects and non-elementals mixed in. Black Mages (magi?) may have access to one or two spells from other elements, Quake, but that's about it. I think Water has made it's way into the spell list of late. Them having access to all elements is more of an XI and XIV 1.0 thing as far as I know.