Criminal Law Questions? Ask a Criminal Lawyer.
I'm sorry to hear about your situation. Unfortunately, no, police are not required to use audio or video recordings to get a conviction. It certainly helps, but the officer can testify as to what occurred. Depending on the jury, that may or may not be sufficient enough to get a conviction.
Generally, speeding is not sufficient for an officer to search your car. Either you would have had to have given consent to search the car, or the officer would have had to had probable cause to believe there was contraband in the vehicle before searching, generally. If neither of those things occurred, then your lawyer might have grounds to file a motion to suppress the drugs.
Finally, with respect to Miranda warnings...unfortunately, television makes it seem like officers must give them every time they arrest a person. However, officers really only have to read them if they are taking you into custody AND they plan to interrogate you. If you were arrested and interrogated without the warnings, then the lawyer could file a motion to suppress any statements you made. But if you were never questioned, or if you were questioned but didn't say anything, then there wouldn't be anything to challenge.