Both are perfectly viable specs. Madness is better sustained single target damage while lightning is better burst and aoe. You'll want to learn both eventually. For leveling, lightning's probably best due to all the trash mobs. For PvP, madness is the clear winner. Way more mobile and it has some nice damage reduction skills.

In general, for sustained single target damage, you'll want to go Madness spec. If you need AoE or burst, go Lightning. You'll want to change up your spec as necessary for individual fights.

They don't get bolstered, but your main character is boosted enough such that you pretty much mow through everybody by yourself anyway.

In the case of tacticals sans tank, it's quite easy for a healer to gather aggro on specific mobs since dps normally don't try to grab aggro on every single target in a fight. Healers can do a decent amount of damage as well. Tanks are known to not do too much damage on mobs, but that's because they spec for endurance rather than mainstat whenever possible. As a healer, you spec for mainstat so your attacks, while lower than a dps, will still do a substantial amount of damage. Coupled with your heals, it is not unlikely that you'll pull aggro off dpsers if they're not focusing on specific targets and are taking a ton of damage for your hots to accumulate threat. In regular FPs with a tank (or just tacticals with a tank), given that you and the tank are similarly geared, it should be completely impossible for you to pull aggro off a tank. That is unless your tank is terrible and doesn't know a good rotation, which is definitely a thing. I personally have never had a healer pull off me in a boss fight when I'm using a tank, ever, but I definitely have pulled aggro off tanks with my operative healer. Heck, if you try real hard, even burst classes like carnage mauraders can't pull boss aggro off you if you have no situational need for your taunts anytime soon.

That certainly is odd. I've played 4 healers through Athiss SM before and no one has ever commented on the DoT at the end boss. I doubt they even know about it since most of the people on Athiss SM don't even attempt to walk a little away from their teammates so that the ending aoe damage doesn't hit everyone.

If you are getting bored of only healing, why not just DPS while there isn't anything to do? I main an operative healer, and when you get to be grossly overgeared for FPs, you become able to heal the tank through most adds damage by just kolto probes and surgical probes. Instead of pulling mobs and potentially angering the rest of the group, I just simply dps along with them. No diagnostic scan necessary.