Morgana Support?
 

How viable is she? Is she good when trading damage in the laning phase with the adc?

not very

and no

Aren't you supposed to go all-in with Morgana support?

She's a counterpick. I'd use her against Sona, Leona, Taric and carries that have lots of magic damage, e.g. Corki Ez,

I'd really only run her with Draven. She keeps someone in place long enough to let him chain his axes, and with her spell shield, cc can't interrupt the axe chain. Otherwise, a standard support will do a better job.

Her shield lols at blitz in lane.

She's extremely good with Draven.

[E] Shen'd :/

fine vs cc heavy lanes like leona, blitz

I use her if the enemy team has Leona.

She's fantastic, albeit a bit difficult. I am almost unbeaten when playing Morgana support. Black Shield counters so much in lane that when playing against half the other supports you can simply say "nope!" to most of their CC and poke, Dark Binding is STILL one of the best poke-initiations in the game and her ult is even better for assisting ganks than it is in mid (due to having 2 targets to affect). Only drawback is that you have to get a Zhonya's Hourglass as early as possible and even with the support buffs that's not easy.