Does Kosmo charge a fee when I get paid?

No. Kosmo does not charge any processing or transaction fees.
When you connect your Stripe or PayPal account, you’ll only pay the fees that apply to either of those platforms. You can learn more about those fees here:

Stripe fees (Currently: 2.9% + $0.30 per transaction)
PayPal fees (Currently: 2.89% + $0.30 for US transactions)