It was formerly known as a "Bad Conduct Discharge" and ranks just above a Dishonorable Discharge.
A Dishonorable Discharge is the the worst fate conceivable.
am I considered a veteran if I have a dishonorable discharge
no
Walt Disney did not receive a dishonorable discharge because he never served in the military.
Yes.
No, he got a medical discharge
You cannot own a firearm with a dishonorable discharge, which is the most severe discharge there is. However, a "less than honorable" is not the same as a "dishonorable" discharge. If the discharge resulted from a court martial, and the service member was convicted of a crime that would be a felony (punishable by a year or more in prison) then you should consult an attorney for legal advice.
In dishonorable discharge, you lose your veteran benefits, cannot reenlist, and are often treated as a felon. In bad conduct discharges, you lose your veteran benefits, cannot reenlist, and are often treated as a felon, but you retain your honor.
The only thing you can do is appeal your discharge.
No.
Dishonorable discharge
Trust me, it is not public record.