I'm afraid it is not correct. She was free to go wherever and do whatever she liked. She was free to go wherever she liked and do whatever she wanted.

I would drop the "to" before "where" -- more of a "parallel structure".

Yes, it makes perfect sense.

I would remove the word "to" before and after the word "go". I would sound less wordy like this though: She was free go where and do what she liked. or She was free go where she liked and do what she liked.