Verify and understand all traffic sources. Make sure you know exactly where traffic is coming from, and if it’s a source that you can replicate after purchasing the store.
Confirm financial info, including expenses (inventory and marketing) of the store. Make sure you know exactly what they are spending to generate the results they are.
Vet their social media accounts. Look at the engagement rate to ensure their following is real. Don’t take a large following at face value.
Know exactly what’s included. Try to get all of the related inventory, social media, email list, etc. if possible. If it’s something that is necessary to run the store, make sure it’s part of the deal.
Understand why they're selling the site. You might not get a reason, but it's still worth asking.
See it for yourself. Use screen-sharing or obtain "view only" account access for necessary verifications (traffic, sales, ad spend, etc.) with the seller.