No, in fact, it is a civil rights issue and a violation of the US Constitution of freedom from unlawful search and siezure.
If you were eventually arrested due to anything they discovered within that wallet, you have the right to have it suppressed, meaning thrown out of court.
This answer is not intended to form an attorney/client relationship and any answers do not constitute direct legal advice and should not be followed unless and until you have spoken with an attorney of your choice.
No and in fact most cops will ask people to remove their identification or whatever from their own wallet.
Although I have answered the question to try to help you, you should consult with a lawyer in your area in person on the matter. In addition, my answer does not establish an attorney-client relationship between us.
No. An officer can pat you down before an arrest if there is fear of a weapon, but they cannot search your belongings. Post-arrest, yes, but not until there is an arrest. If during the search the officer found something illegal you should challenge the illegal search.
NO! You should contact the officer's agency and file a complaint. I would not put more into the complaint than to say officer "X" stopped me; did a pat down and then illegally removed my wallet and searched it. You do not need to supply why the oficer stopped you.
The above is not intended as legal advice.