How do I clean the inside of my frame? Is it even necessary?
The most important thing is that there is no standing water inside the tubes. Usually there are drainage holes around the rear dropouts and bottom bracket. Make sure the holes exist and are not obstructed.

You can look inside the frame through the bottom bracket, seat tube and head tube. Some people use oil or wax-based surface treatments against rust, e.g. J.P. Weigle's Frame Saver.