Was Kirk negligent for not monitoring the conditions in which he left Khan on the planet Ceti Alpha V

Kirk no, Starfleet maybe. The problem is that by monitoring, you risk contact. That is something you don't want.

It seemed the most rational and humane thing to do, let Khan go on a remote planet.(The MOST rational would be to kill him)

No, Khan wanted his independence and authority over his pals above all, and if he knew he was being checked on he would have both resented it and tried to hijack the monitoring ship. And if any rescue had been attempted he'd have tried to hijack the rescue ship.

Khan was a few pom-poms short of a cheerleading squad at that point, his anger no longer had a rational basis, it was just pure anger focused on a convenient target.