I'm up to level 24 as a healer and still having no real problems. I mostly DPS while questing (luckily Supercharged Cells is both a dmg/healing buff so I can do not awful dmg if I must) except on elites/class quest bosses, where I dmg control/heal my companion.
I just got my tank companion, and tried him out, but while he can hold aggro like a champ, I found the first companion you get (ranged DPS) tends to be more useful. The tank is pretty squishy out of the box (a trooper with cybertech could make him gear, but I haven't come across most of the gear he wears while questing to get him upgrades), and his DPS is much lower than your first companion's.
As far as actual healing goes, I've only healed PUG heroic quests, not Flashpoints so far, but what I've experienced is a lot of "omg why are my heals so slow?" where people are taking damage faster than I can heal them. However some of this is that my groups were largely not using CC, and I've been told by others that this is a game that loves CC. This may be true as most of my troubles have been with bad trash pulls and not with boss fights, which have largely been easy enough to heal that I have been able to help DPS. Also, having a real tank helps, and I haven't always.
At first I had trouble constantly running out of ammo, but the Supercharged Cells talent/ability and the talent that makes Medical Probe give stacks of Combat Support Cell has helped a lot with this.
Attacky stuff to keep on your healing bars even though it's not healing: Cryo Grenade (stun), Concussive Round (CC - pretty much Polymorph with a Repentance style CD), Concussive charge (knockback), and maybe Sticky grenade (good for dealing with weak/standard adds).
As far as secondary stats go, the ones that benefit us are:
Tech Power (which I've only seen on weapons/off hands so far) and Power improve your +healing
Crit is crit (and once you talent into it, crits can proc extra alacrity)
Alacrity is haste - i do not know if it affects ammo regen or is just for faster cast times.