Token collector objective

I assume that Gems are a random spawn of Power Ups. You can see I'm interested in the spawn rate of Power Ups myself.

Given that Gems are treated the same as other pick ups, you can increase the chance of spawning them with the "Pickup Spawn" boost in the "Abilities" menu for each character (when the boost is purchased it is permanent and applies to all characters).

Pickup Spawn

Spawn X% more frequently

Where X increases in steps the more coins you spend.

Although the world HS will always change, to view the current one, try looking in Game Center for the leaderboard for Worldwide: many games often have a worldwide leaderboard visible there.