The toilet handle falls off the bar that connects to the chain inside the toilet tank. If I replace the "insides", will the parts include a new handle?

The handle is available as a kit and so is the water valve/manifold. Good luck.

When you buy a handle for your commode it comes complete with the handle and the arm that the chain attaches to. Just remember that the nut holding the handle in the commode is a left handed nut and will turn backwards from most nuts.