Ambiguity of regular expressions
Yes, every regular expression can be converted into an unambiguous one by converting to a DFA and then to a regular expression. And no, there aren't any inherently ambiguous regular languages in the sense described in the question. This is a classic result in automata theory:
 R. Book, S. Even, S. Greibach and G. Ott, Ambiguity in graphs and expressions, IEEE Transactions on Computers 20(2) (1971) 149–153. 
See also this question over at MO for more details and a reference: https://mathoverflow.net/questions/45149/can-regular-expressions-be-made-unambiguous