Does my new phone come unlocked

1. Purchase Apple Products from the Apple Online Store, Apple Retail Stores, and many Apple-authorized resellers and wireless service providers.
2. If you choose "Connect to a carrier later" (Unlocked iPhone) when you buy your iPhone, you can activate your service when you receive your device with any Carrier of your choice.

Yes, unless the phone was tied to a carrier as part of a special promotion.

Check your sales receipt for details.

That would depend if you bought an unlocked phone or one that was subsidized by a carrier. Call the store you bought it at and ask them.