To address the first issue; should you disclose? No. You are not required to, nor should you. You were never required to disclose those facts on the form.
14 CFR 67.403 provides that falsification of the airman medical application form 8500-8 may result in enforcement action (which can include fines up to $250,000, imprisonment up to 5 years and revocation of medical and all pilot certificates). This does not apply to you, however.
The FAA is interested in a history of driving while impaired, or any violations or convictions for use of a controlled substance. Unless your traffic ticket resulted from driving drunk or on medication, or for being impaired in any other way, it's not relevant. Unless your juvinile alcohol event is related to motor vehicles, it's not relevant, either. Additionally, your juvinile record is sealed, although not from certain databases.
The only relevant questions on the FAA Airman Medical Application Form 8500-8 are lines 13, 18

, 18(o), 18(v), and 18(w). See the form at
http://www.leftseat.com/pdffiles/8500-8a.pdf.
Line 13 specifically refers to previous revocation or suspension of your FAA
airman privileges...not driving. It has nothing to do with driving, nor with any former misdemeanor felony convictions. Strictly the history of your FAA airman (pilot, mechanic, instructor, rigger, flight, air traffic controller, etc. certificates). Line 13 does not apply to your situation or question.
Line 18

asks about your medical history, specifically the issue of substance dependence. This can be alcohol, or any other substance to which you have ever become dependent.
Substance dependence is defined by any of the following: increased tolerance, withdrawl symptoms, impaired control of use or continued use despite damage to health or impairment of social, personal, or occupational functioning.
Substance abuse includes the following: use of an illegal substance, use of a substance or substances in situations in which use is physically hazardous, or misuse of a substance when misuse has impaired health or social or occupational functioning.
"Substances" include alcohol, marajuana, PCP, cocaine, amphetamines, barbituates, opiates and other psychoactive chemicals.
Line 18(o) specifically points to alcohol dependence or abuse. Note that Section 18 of the medical application form doesn't ask if it's been in the past few years...but if you have ever had any of these conditions. In the case of alcohol, if you have ever been an alcoholic or had an alcohol problem, it's relevant. One does not stop becoming an alcoholic. One may go the rest of one's life being a recovering alcoholic, but one doesn't stop becoming an alcoholic. Therefore, if one has any history of abuse or dependence, it's relevant, and the FAA wants to know about it.
In your case, if you had an alcohol related offense as a kid, it's not relevant unless you had a dependence issue or an abuse issue.
Line18(v) most closely addresses your question. It specifically asks about a history of any conviction involving driving while intoxicated by or impaired by or under the influence of alcohol or a drug, or any history or conviction or administrative action involving in offenses which resulted in the denial, suspension, clcellation, or revocation of driving privileges or which resulted in attendance at an educational or rehabilitation program. Quite a mouthful, but there you have it.
Subparagraph (v) wants to know if you've been convicted of an offense involving driving under the influence. That can be alcohol, drugs, etc. That conviction may include a fine, forfeitting a bond or collateral, etc. A formal conviction isn't necessary. Defaulting on a ticket and being convicted in default under Failure to Appear is enough. Ever get tagged, released, and never went back to clear it up? In that case, this may very well apply to you. From your description, it does not.
Subparagraph (v) also asks about conviction or administrative action by any jurisdiction for which your license was denied, suspended, cancelled, or revoked. It also asks about any conviction which resulted in attendence at an "educational" or rehabilitative program. You are
NOT required to report individual traffic convictions if they did not involve alcohol or a drug; suspension, cancellation, revocation, or denial of driving privileges, or attendance at an educational or rehab program.
If you did get a suspended license (or revoked, cancelled, or denied) for any reason, not just for alcohol or drugs, you must report it. Same if you had to undergo a reeducation program or rehab program in connection with a conviction for a traffic offense.
If you answer Yes to Subparagraph (v), you must provide an explaination. This must include the drug or alcohol offense for which you were convicted, or the type of administrative action involved (for example, attendance at an alcohol treatment program in lieu of conviction, license denial, suspension, cancellation, or revocation for refusal to be tested, educational safe driving program for multiple speeding convictions, etc). You must also provide the name of the jurisdiction involved, and the date of the conviction or other administrative action (school, etc).
On line 20, you provide the FAA with authorization to check and verify your records against the national driver database.
Subparagraph (w) enquires regarding non-traffic violations or convictions. These may include assault, battery, public intoxication, robbery, etc. You must provide the charge for which you were convicted, and the date of the conviction. Note that this subparagraph doesn't ask about arrests, suspicions, or anything other than a conviction. I mention suspicion, because in many jurisdictions, being associated in any way with a crime or inquiery will result in you having a record as a "suspect" in local or state police files. This doesn't mean anything, and should not be reported (and chances are, you'll never know about it).
In the case of the man who beat his girlfriend; unless he was convicted, he won't have an issue on the FAA Airman Medical application. However, if he holds an ATP certificate, he may risk suspension or revocation on the grounds that he has not shown good moral character.