Yes, they will give you store credit. Be sure to double-check with the store.
Yes, items can be returned if not used with a receipt. You will be refunded in the same way you purchased (cash or credited to your CC). I think it's up to 1 year. Also if you use something and it's defective, bring it back. I have found IKEA to be very good at standing behind their products as long as it's not something that the customer has clearly misused.
Yes of course you can return something without a receipt. But they can only give you store credit. Hopefully that'll be ok for you because they have so many cool things to choose from.
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