Do cops have to personally present you a moving violation ticket?

You’re lucky you don’t live in Australia or New Zealand where the registered owner of the vehicle is liable for the fine. I believe in Australia (but not NZ) that the owner also gains demerit points on his or her license if nobody owns up as the driver.

In Ohio, not necessarily. But an acknowledged interruption in the officer’s period of observation, coupled with a credible defendant insisting the officer mistook one car for another, may very well give rise to reasonable doubt, and lead to an acquittal. Depends on the court, the officer, the defendant, any other witnesses, etc.