You can enhance your privacy when browsing and posting to this forum by using the free and open source Tor Browser and posting as a guest (using a fake e-mail address such as nobody@nowhere.com) or registering with a free, anonymous ProtonMail e-mail account. Registered users can exchange private messages with other registered users and receive notifications.
With that in mind, you need to understand that the questions that concern you are probable-lie "control" questions. Rightly or wrongly, everyone is assumed to have done such things as cheating in school or driving while under the influence of alcohol. The polygrapher will steer the examinee into a blanket denial because he actually wants the examinee to be less than truthful when answering these questions. The examiner scores the polygraph charts by comparing the examinee's reactions to these assumed lies to his/her reactions to the relevant questions.
Although admissions to the things you mentioned would be highly unlikely to disqualify you (again everyone is assumed to have done them), you would be better off not mentioning them should you proceed with the FBI polygraph.