As beautiful as = τόσο όμορφη όσο, while σαν=όπως=as without the comparison in quantity, but only in likeness. I don't think it is exactly the same as you would translate σαν with a comparison like the one given above.
No, because there's an είναι implied there: είναι τόσο όμορφη όσο (είναι) η μητέρα της / she is as beautiful as her mother (is). Have a look here: whatever your take on the English grammar is, this is the only way it works in Greek. :)