My question involves criminal law for the state of: New Jersey

Let's assume that I'm totally alcohol and drug free and a cop wants me to take these tests. I understand that field sobriety tests are designed to fail. I know because I was falsely accused of drugged driving and the officer said I failed the tests. I think I also have genetic nystagmus which they always check for. I wouldn't refuse a breathalyzer or any chemical drug tests.

Could I be convicted if I failed all field sobriety tests, but passed a breathalyzer & chemical drug test?

Also, should I give consent for a cop to search my vehicle when there is nothing illegal inside. I'm afraid that they could plant drugs.