Legal Question in Criminal Law in California

Yes, or your attorney must appear for you.

Yes, unless you are represented by counsel. If neither appear, the court will issue a bench warrant for your arrest.

Either you must appear or your attorney (with only a few exceptions) can appear on your behalf. If it's a domestic violence case, you must appear at the first court appearance. If the judge orders you to appear (some judges require your presence on a second or higher DUI), then you must also appear.

If you're asking whether you can appear by mail or just pay a fine like a traffic ticket - the answer is no.

Of course, unless you are willing to have an arrest warrant issued.