Shadow isn't any more lethal than Holy/Disc until you get to level 40 and get Shadowform. That's when the difference in damage output becomes significant.
Personally, my rotation was (and is) Shield-Holy Fire-SWP-Starshards (it's really mana efficient damage spell)-Smite-Wand. If mob has a lot of HP or is orange, then add MB as well as extra casts of Smite or perhaps another Shield. The more talents you get that increase Holy damage/crit chance, the less you should use Shadow spells, obviously.
I'm 58 now and didn't have much trouble but this approach certainly requires patience. Especially when you see mages 2-shot mobs

Very little chance of soloing elite quests, though you should be able to get a group together easily - the magical "Healer LFG ---" works pretty well. Healing instances has been a piece of cake, though I haven't been in LBRS/Strat/Scholo yet, but this would suggest that healing 5-mans in Shadow specc is quite viable.
PvP-wise, we'll you're a free HK most of the time, though if the other guy is fairly inept or of lower level, the ability to heal/shield and dot occasionally manifests in hilarious reversals - had a 60 troll mage chase me halfway across Barrens and deep into Ashenvale few days ago, he just couldn't slow me down thanks to Dispel Magic and with Renew and Shield up I stayed at 100% HP almost all the time. Similarly, the healing prowess is fantastic in those situations where you get into a PvP tussle with a group - unless the other side quickly spots and nukes you (which is annoyingly common), you can easily keep 3-4 guys up while they slaughter the opposition.
Hope that helps.