And because I don't know what you do know I hope this isn't redundant, but isn't Squarespace an online make it yourself hosted solution?
If so, did you buy your domain name from them? Do you have access to the domain name to use with other hosting providers?
If so at some point in the process you will need to change the name servers to your new hosting plan.
You will need to have that (your domain name) and a hosting account.
You will then need to install WordPress on your hosting account.
And set it up with what ever theme you find.
The links about backing up your SqSpace and importing should be helpful.
So :1. Say our URL is url.com (for example). Will the URL stay the same after migration?
If you own the url and have access to it beyond SQSP --- yes
2. We've email accounts linked to the site (e.g. firstname.lastname@example.org) - will these be affected?
Depending on how they are set up, you should be able to forward mail to a new account // and you can set up multiple email accounts on most hosting plans (again depending upon what you buy)
3. Is WordPress installed over/replaces Squarespace?