Nick here from Shopify.
I understand that this is quite a frustrating situation to find yourself in. However, for the privacy and security of all merchants using the Shopify platform, we wouldn't be able to give out any specific information on any store nor can we confirm if they are using our platform to host their online business. However, what I do suggest is to contact the store owner directly from the info provided on their store. It looks like you have already done this to no reply though. Do you mean it's been 10 days since your order or since you reached out to the store about your order?
If you don't hear back from the store, the next best steps are to reach out to your bank about it. Your bank will have measures in place for you to follow in this case and will be able to help you in relation to the payment made from your account.
We have a community topic with some more information and steps to take in this exact situation which you can find here.