yesterday I tried to connect my WooCommerce/WP site so Shopify and did it successfully.
But when I saw that my former website was not working anymore I disconnected it from Shopify.
Now, after a few hours down, mywebsite is working again but seems showboat still connected to Shopify because a see Shopify favicon when I open my website.
How can I COMPLETELY disconnect my website from Shopify??
It sounds like the DNS information for the domain needs to be updated to ensure that it is pointing to the correct website. When you connected it to Shopify, the DNS would have updated to point to your Shopify store, then once disconnected you would need to edit the DNS settings for the domain to point back to your previous store account.
The issues you are having with the www and non www version of the store URL are directly related to DNS issues as well.
You will want to check the DNS settings for Woocommerce/WP and sign into your domain host to finish updating the DNS. It can take 48 hours for changes to the DNS to update as well, so once you add the right dns fields you will need to give it some time to take effect.