1. Does Sharpshooter work on thrown weapons?

Yes, as long as a ranged weapon mentions a range, it will work since a weapon can have both the thrown property as well as a range. Case in point, the spear can effectively be hurled within a range of 60 long and 20 short.

2. Does Sharpshooter ignore prone?

No, a prone creature will impose a disadvantage on any attack against it farther than 5 feet. The 5E Sharpshooter’s range clause considers only the disadvantage imposed by long-distance, not other sources.

3. Does Sharpshooter double on a crit?

No, the +10 is a static bonus and not a rolled damage. Critical hits will allow your character to roll double the damage.

4. Does Sharpshooter work on spells?

No, it doesn’t. If you are interested in something of this sort, the Spell Sniper feat might be worth a look.

5. Is Sharpshooter overpowered?

While the Sharpshooter feat is quite powerful, it is certainly not overpowered. It is a necessity for ranged combat classes. Moreover, clever Dungeon Masters can find ways to maneuver around it and mitigate some of its benefits, if necessary.