Connection String Question

I have number of web instances in IIS server, where these websites uses connection strings to connect to the SQL Server data.

There is single web.config file for all the website where there resides connection string which used by these websites.

Few websites have its own web.config file where these uses connection string from this rather than using from common web.config.

My doubt it, when we take the properties tab and click on general. We can see Connection Strings over there with the values. We can create and edit those.

Is this related to the connection string in web.config? If we edit it ,,will this effect in web.config? How can we know which web.config this value is showing in IIS setting , whether in common web.config or web.config of individual web instance folders?
can we add a new connection string in IIS rather than adding in Web.config file?