Neither may be required. If the officer's signature is required then the citation may be dismissed. You should contact the court listed on the citation for information .
the police officer gave a citation
GENERALLY speaking, the officer certifies the citation with his signature. If there is a specific place for the officer's signature and he did not sign the citation, you may want to ask the court to dismiss the citation. The officer may be allowed to re-issue the citation, but it is fairly likely that specific ticket is not valid.
Yes. a officer can issue a citation in any location.
If the stop results in a criminal charge or citation, yes, the officer must inform you of what you're being cited for. If the stop does not result in a citation or punishment, the officer does not have to inform you.
it can be discharged
If by this you mean Driving Without Automobile Insurance, and you received a citation from a Police Officer, then yes, it is. Any time you receive a written citation from a police officer, it is considered a "Misdemeanor"
It usually can be mailed.
The defendant cannot change the citation notice before or after they sign it. The issuing authority (usually officer) completes the citation notice.
If the officer does not appear when required, the citation is usually dismissed. But the officer is not always required.