The first ability triggers when you cast Prossh, not when it enters the battlefield. This means that it will resolve before Prossh, so any Kobold tokens it creates will be put onto the battlefield before Prossh. If Prossh enters the battlefield without being cast, the ability will not trigger.

You can't choose to pay extra mana to cast a creature spell unless something instructs you to.

The amount of mana you spent to cast this creature is usually equal to its mana value. However, you also include any additional costs you pay, including the commander tax.