Q: If the police want to search me, my home or my car, should I give them permission.
A: Not unless they show you a search warrant.
The 4th Amendment to the United States Constitution guarantees you, as a citizen of this great nation, the right to be free of unreasonable searches and seizures. If the police violate your rights under the 4th Amendment, all the evidence that they have obtained as a result of this illegal search and seizure is not admissible against you at trial.
If the police ask to search you, your home or your car, say loudly and clearly that you do not give them permission to conduct the search. They may search anyway. But at least you have not given your consent to the search. If you consent to the search and the police find evidence of a crime, it is unlikely that any court will find that the police violated your rights.
Cooperate with the police at your peril.