Can I see the location or path of my iPhone for the last 24 hours?

Not unless you can find an app that tracks that info. Apple's find my iPhone system only gives you the current location, or last known for devices that are offline. It does not provide historical tracking data.

There are apps that track in real time, and record that info on the iPhone (although I don't know of one that will transmit that information anywhere, but there may well be such an app). Keep in mind that anything like that will eat up your battery life very quickly. Find my iPhone does not kill the battery as it basically only sends a location fix to Apple when asked for one by the server. So most of the time find my iPhone is NOT using location services, but is simply waiting to be pinged by Apple's servers when an authenticated user asks for the devices location.