With most domains, you can get your purchase refunded within 5 days of the purchase if you call support. They can use the credit from that refund to help you purchase the correct domain name.
Yes, a new purchase. You can't change the spelling of a registered domain. If you want it to be something else, you will need to register the name you want as a new domain. As previously noted, most domain registrations can be cancelled and refunded if removed in 5 days (exactly 120 hours) from purchase. You'll need to contact customer support to be credited for the misspelled domain, if allowed by our refund policy.