Can I pay a shoplifting fine and not go to court?

You always have the option of pleading guilty to the offense and avoiding the necessity of the prosecution having to put on a trial to prove you committed the crime. The punishment you will receive upon the entry of your guilty plea will be left to the judge's discretion. It will normally include a fine and court costs, as well as jail time (which may be suspended) and some kind of probationary period.

No. A shoplifting charge is not a traffic ticket. You must appear in court. You should discuss the specifics with a lawyer as soon as possible.