I have a business website, www.stockrumors.com, and it is a pretty simple design on the user side of things but the back end and admin side of things are a bit more complicated. Is it possible to create a new site with Squarespace and link the back end functionality to that site so as not to lose any subscriber or database information?
It is definitely possible to convert an existing site over. What SquareSpace can do for an existing site is give it a really nice front-end editor for layout, etc. However, while SquareSpace does host the site, they don't host databases.
What that means is even if you move to SquareSpace, you'll still need to host your own customer database. As a result, you won't lose any customer data functionality at all considering the backend for your database can use the same setup it currently does.
If you want to try out SquareSpace, they have a free, two week trial period; play around with it, and see if it will work for you.