Does it change the shopping cart buttons if we change the website URL?

The product buttons functionality will be affected when you change your Console URL (website prefix), but only for purchase buttons that you implemented on external websites. If you have Console product buttons inserted in an external website, after you change the Console URL, you need to take the purchase button code for the product again from the product settings in the Console system (Billing menu > Products > edit product > tab 'Publish') and re-insert it in your external website. The link in the purchase buttons that you have on your Console website will be automatically corrected (updated) when you change your Console URL.