First off:
Gearwise you can start Naxx10 in your L80 quest blues. You won't do great dps, but as long as you're not an idiot you should do fine.
In regards to trash between bosses. Some are simple extensions of heroic dungeon trash. Stay behind the mob if you're melee dps. Don't pull aggro. Don't pull additional mobs. If there's a ton of mobs to be dps-ed, do some AoE dps. If you're gonna do AoE dps (as a shaman, magma totem is the one I think), wait till the mobs hp visibly gets under 100%. That way you'll definitely not pull aggro.
Then there are "special" trash mobs like:
- Frogger: Frogger is an old computer game where you played a frog that had to cross the street by dodging cars (or he'd get squished). In Naxx (right after Patchwerk) there are
slimes that explode if you get too close. This WILL kill you unless you're a paladin in a Divine Shield. Trick is to run between them (like in the game Frogger)
- Super-fast respawn area: There is a room (before Loatheb) where mobs respawn incredibly fast. So the only thing you can do is let the tank run through as fast as he can, body-pulling enough mobs to enable the rest of the raid to run through unharmed. You then AoE the pulled mobs once at the exit (any sooner and you'll pull aggro).
Explaining that you're new ensures ppl will instruct you before tricky encounters (or you can just say it's been a while and you might need a "refresh here and there"

).
As for multitasking. Let me ask you this:
In the first part of DTK (heroic or not) some mobs cast Void Zones (black circles) on the ground. If you stand in it you take damage, so you run out.
If you always seem to die there you wont do well in raids...
You don't dps the boss, dps the adds, spot heal AND run out of the fire all at the same time. Usually you will have ONE role to fill and one main target that gets priority.
Example:
Maexxna (huge spider, boss of Spider Wing)
At first you dps her
then she spawns little spiders (you drop a Magma Totem for them)
and you continue to dps her
Don't heal unless you REALLY have to (healer very low on hp). Trust that the healers will be doing their job.
You MAY get asked to heal AND dps on one of the four horsemen.