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Solo friendly: no. You can solo, but its extremely tedious and frustrating.
You can LEVEL solo, and quickly, depending upon your class. But you wont see the inside of dungeons this way, or at least not much. A Bear Shaman, Disciple or Necromancer, in good equipment also Dread Knight might manage the easier dungeons solo, but you wont see them call it fun. Cleric can too, but OMG is that slow.
Duo, well, that depends upon your setup.
Real Tanks are Paladin, Dread Knight, Warrior. With limitations Drunken Monk, Bear Shaman and actually Disciple can operate as tanks. Cleric could too, if they had any way of keeping aggro.
Real Healers are Cleric, Shaman, Disciple and Blood Mage. Druids have some emergency healing thats not too bad. Paladins have some not completely irrelevant healing. Rangers have some healing spells that I would actually call rather decorative.
Tank and Healer works very nicely, especially if they are "real". It will be slow in dungeons, but you can always try to find some more people to improve damage output.
Healer and damage dealer, well that kind of works, more or less. Especially if the healer is a Disciple, because they can actually work like a kind of lesser tank in many places, fetching tons of aggro from their constant self healing.
Tank and damage dealer, well that kind of works for Paladin and Dread Knight, since they have some self healing. So they can tank and heal themselves, and the damage dealer makes it much more fun. Bard is a good second for this, because they can boost the damage of the tank as well, and provide some healing (through increased health regen) if necessary (but they need to use an instrument for this and wont offer much dps anymore this way).
Damage dealer combos that work, I dont know any. Maybe drunken Monk and Druid ?!? Of course you can always kill faster than anybody else. Sorcerer and Ranger could probably AoE clean stuff in record time.
Favorite setups I tried or heard about:
Warrior and Blood Mage
Dread Knight and Bear Shaman
Monk and Disciple
Paladin and Bard
Best tag team?
Pally and DK
Other Duo classes I like are
DK + Disciple
Ranger + Ranger Outside kiting and super fast power leveling.
Monk + Shaman Bear
Necro + Necro fear kiting rotation
I have great success duoing with my wife.
I am a Disciple and she is a Necromancer.