I would not buy from or sell to Gazelle regardless of what they claim.

No. I bought two iPhones that were supposed to be excellent condition phones and both had major issues and I had to return them. They were very good about refunding my money, but to advertise them as excellent and both had issues worried me. I did not buy a third phone from them. They have these great reviews on their website, but if you look elsewhere, they get really bad reviews. I would be cautious buying from them.

I would not trust them.

In general regarding warranties on Apple iPhones, Apple is the only provider that sells the AppleCare warranty package. Other providers, Walmart, etc., also sell warranties when you purchase the phone, but those warranties are not the AppleCare warranties, it is a warranty provided by other warranty companies.

Don't buy from gazelle! We had good luck with cellphonecity.com. Gazelle has not refunded my money from late October.