Most of the early Dwarf and Elf quests in Ered Luin seem to be based on The Hobbit, so doesn't that mean they do have the license?

You're right there, actually. I've always been confused about this since they say their license is from SCZ... and I confuse what they own and what Christopher Tolkien owns.

Tolkien Enterprises is a trading name for Saul Zaentz Company (aka SCZ) and they own the rights to both the Hobbit and LotR. I'm not sure if Turbine's agreement with them covers the Hobbit per se, but I'd be surprised if they'd not be open to the idea if not.

That would be cool.

Yes,

Turbine has the licenses for both LotR and the Hobbit.

http://www.massively.com/2008/02/20/lots-more-lotro-to-come-turbine-extends-lotr-license/