Grenades are incredibly useful in bad situations or when you find a bunch of enemies. Cluster grenades set off biotic explosions, but you have to use another power like warp or reave to initialize the explosion. I have cleared out whole rooms of enemies with a single throw of cluster grenades after using reave.
Singularity is a glorified version of pull. In fact you can either set it up to be very similar to pull or you can make it effective at pulling enemies out of combat for a little while. The only difference between pull and singularity is that pull has a slightly faster recharge time and singularity can explode at the end of its duration.
Shockwave is one of the weaker biotic powers in mass effect 3. Whenever you use biotic powers your main objective should be to set off biotic explosions which can often kill enemies. Shockwave makes it very difficult to even hit an enemy and when it does it only deals 300 points of damage max. In comparison the vanguard deals 375 with charge and up to around 1000 damage with nova. Shockwave is very useful against groups of enemies because it deals damage over distance regardless of how many enemies it hits.
The war asset readiness rating is an indicator of how good your war assets will perform in the final battle. So the effective power of your war assets is the amount of war assets multiplied by the readiness percentage.