will a refurbished iphone work outside of the US?

If it's a refurbished iPhone purchased directly from Apple, then it will come with the full standard one-year Apple warranty (AppleCare can be purchased to extend it). Whether the warranty will be honored in your country depends on your country and to a certain extent the nature of the problem. Check with Apple Support in your country to inquire.

As to whether it will work with your local carrier, it will depend a bit on which specific model of iPhone you get. Newer ones only have eSIMs and not all carriers around the world support eSIM. Confirm support for the model of iPhone you're considering with the carrier in your country that you plan to use.

If you purchase a "refurbished" phone from someone other than Apple, then there's no way to be completely sure what you'll get and whether the phone will come with problems. No third-party vendor can do a true refurbishment, and what one vendor calls "refurbished" may differ greatly from what another vendor will do.

Regards.

i plan on getting a phone from the 14 series and it says in the store that it is “unlocked”, so just to confirm, does that mean that i can use my local carrier? they allow esims as well.

In theory, the phone will work. In practice, you won't really know how well it will work or....if....it will work....until you ask the carrier that you intend to use whether they will support a phone designed for use in the U.S.

Even then, you cannot know if the phone will work until you actually try it out with the carrier that you choose.

Probably, but it would be best to confirm with your carrier before you purchase.

Regards.

Please keep in mind that that a phone purchased in the U.S. will have no warranty outside of the U.S.

Our advice would be to always buy a phone in the country in which it will be used most of the time.