For REAL information on the Ohio points system check out http://www.state.oh.us/odps/division/bmv/mvdigest.html
Basically there is a sliding scale. If it is your first speeding offense in the last year it is a 2pt violation. If not it depends on how fast and how many violations you have - see the chart on page 46 (51) of the PDF file they provide. As to fines etc your mileage may vary, i.e., local laws vary as do judges rulings. If a 2pt does not bug you, i'll bet that if you contact the court they will let you pay via mail/VISA as you live so far away.