As far as normal mobs beating on the healer, It's the tanks job to hold aggro on the more threatening mobs, silvers/golds/champs/boss the normals should be killed first by the dps which is why most tanks will maybe hit them with an aoe or default attack just to get initial aggro. But it's really the DPSs job to know the kill order and actually do it.
That is the most important thing. I got told on my Juggernaut for not holding aggro on the weaker mobs. I throw in a Smash and then I continue my way on to the silvers and golds, indeed.
And when it comes to healers doing damage. I often throw in a Death From Above (When the healer is topped and still has enough charges of Kolto Shell). I know when I can do extra DPS on my healer and when I just focus on healing and don't bother with doing damage.