Doesn't Asume resemble Auzla?

I think she doesn't. All I can see is hair similarity, not facial similarities. ASAME looks like that because she's based on Lust.
And if your thinking that Asame can be Azula's granddaughter, then you fail. Cuz according to Asami her family was attacked by firebader...

You mean Asami.

I believe she does, in a way. She has the mouth and sort of the eye shape. She also has the black hair. I think she resembles Jun more though.

i dont think she looks like azula but she did say that her and father were not benders

nope I think they look completely different

Nope. I think Azula's character goes beyond beauty and 'prissiness'. She just has this certain allure that Asami is lacking. I suppose her wickedly evil ways adds to the appeal too. ^^