Claire's daughter is right about the same age, so she would tend to go more maternal, but she's good at balancing that with knowing just because youth are Youth-y they don't always need to be mothered. She tends to meet people at their level; if they seem young and unsure, she'll be more maternal, if they're curt, she'll be short in return, etc. etc.

I don't know that Claire would know anything about music of the 18th century (other than the [fictional] Ballad of the Woman of Balnain who I think is her mom but that's a theory for a different post), because she didn't have much down time to just be leisurely. It was a constant battle to stay safe for 3 years before she went back to the 20th century and ultimately America. Then when she went back in time again, she spent all of a couple of weeks in Scotland before she was on a ship to Jamacia. Later in her canon she'll have settled in the backwoods of North Carolina, but she isn't there yet.

She DOES know a lot about myths, historical moments of significance, was probably there when they unearthed a few tombs in Egypt, etc. So Teddy can feel free to grill her, and Claire would answer everything to the best of her ability. And if she can't answer it, she knows someone who can, and she would tell her to seek out a man called The Doctor!