You are required to give biographical information about yourself, such as your name, DOB, address, etc. if asked to by an officer. No, you don't have to answer any questions on traffic stops other than those mentioned above, and yes, the police have a right to deny your lawyer to come to the scene of a traffic stop.
Edit: A quick Wikipedia search would have been beneficial here. I found you a sentence that I believe answers your question:
"However, police are only required to warn an individual whom they intend to subject to custodial interrogation at the police station, in a police vehicle, or when detained. Arrests can occur without questioning and without the Miranda warning—although if the police do change their mind and decide to interrogate the suspect, the warning must then be given."
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