Augh what is an omaase

御ませ: Precocious child.

Isn't that a good thing?

I think I'm about as confused as Chie.

It is a good thing. Nanako's trying to cheer Chie up by calling her "precious child"-san. Maybe "good girl" would make more sense.

It's scary how well the Yotsubato! art style suits Nanako and Chie.

Source on pixiv found! This seems pretty great, so I've uploaded the bunch of 'em and pooled them up.

Precocious, not precious.
In the chapter of Yotsubato this is parodying, Yotsuba (Nanako) goes to ask Fuuka's (Chie's) mom what heartbreak is, and Fuuka's mom says "My aren't you precocious."
So not fully understanding, when she tries to cheer Fuuka up, she calls her precocious.

Ok filled the rest in.

Why is Chie in the Doujimas' living room?

Devonian said:
Why is Chie in the Doujimas' living room?

if you read Yotsuba&, its actually Fuuka(Chie)'s house.

Devonian said:
Why is Chie in the Doujimas' living room?

Because there's no other home interior shown in the whole game?

Chie will stand on these two legs.
The fat legs.