third party domain and hosting issue

I have a website built on Squarespace, but my domain is provided by third-party.  I understand that I can connect the third party domain to my Squarespace website, but after doing this, is the website hosting moved to Squarespace?

And, before the connection of the third party domain, can I set the domain and url under the production of Squarespace site before publish?  Or I can set the domain and url of the Squarespace site only after the domain has been successfully connected?