Water doesn't flow "down" where the earth curves a distance away from you because "down" is towards the center on any given point on a globe- the direction gravity pulls it. Your position looks "down" to someone that's "over there".

As for preventing you from exploring, no one is. Hop on a ship or a plane (heck, buy your own) and take off for somewhere... anywhere. If the earth is flat, then every single commercial pilot in the world is in on the conspiracy. Globe is why you fly north towards the pole and back down when you go between North America and Europe- it's shorter than going around, something you wouldn't have on a flat disk.

Anyway... just a couple points to think about.