Can I sell my iPhone, or can I only sell it if I buy another one?

This is a user to user forum, you are not addressing Apple. We users do not buy used iPhones.

You can use Apple's Trade In program and get a gift card for the value of your device. There is no requirement you get a new iPhone.

See here: Apple Trade In - Apple

Apple will not give you cash money however, only a gift card with the value of your device, which you can use to buy anything you want in their stores.

In most cases you will get more for your device if you sell it privately however.

Depends how you bought it.

This forum is not for sales.

If you paid cash or credit card for device and you own it, you can sell, if you are on a plan with payments you need to take up changing phone with provider.