What is the difference between "Vypadám stejně dobře jako ona" and "Vypadám stejně dobře jak ona"?
None. Both are acceptable. I would always say JAKO myself, just flows easier but it is optional
I believe the English should read “... as good as SHE” to be grammatically correct.
"She" is grammatically correct, and "her" is much more widely used. In the reverse exercise, both are accepted.