Singularity is amazing. First off, biotic explosions are triggered when two biotics are combined on the same target. You can do them yourself, BUT, there is a caveat. The first biotic attack has to have a lasting effect (Warp, Singularity, Stasis, Reave, Pull) because it needs to last until the second biotic attack hits it. The second biotic attack can be just about anything (EXCEPT for the same attack, you can't do the same move twice in a row) - I think I saw a biotic explosion come from a pull and a charge.
Which leads me back to my point. Singularity is awesome. The majority of troopers have no shields, so I set 'em up with a singularity, then either warp or shockwave (depending on the range). Which shielded enemies, I usually drop a singularity at them, which stuns them, then I unload with my SMG until their shield gives in. They're usually still stuck in the singularity's range, so they caught in it. Then, BOOM, warp for the biotic explosion. Most satisfying kill ever.
Anyways, I just bought a veteran pack and FINALLY got a new race. Quarian Engineer. Not exactly what I wanted, but it's a step in the right direction.