No, the flute is much higher than the saxophone and gets up to higher octaves. The most equivalent instrument to it's own kind would probably be the oboe. Piccolo is the highest instrument, which is...
No actually the clarinet has a lot of low notes. It is harder for a person who plays the clarinet to play high notes.
Yes, because it is a smaller instrument, and sound waves have less room to vibrate.
Piccolos produce a higher pitched note than a flute because they are shorter, and smaller
I'd say Clarinet. But it depends really.