To answer your questions one at a time:
How secure ConnectionString is over the HttpRequest?
You will never have to pass the connection string through HTTP; it usually happens that the user makes a request, your site processes the request, including connecting to the database, and returns the result to the client. The connection string should not be transmitted over HTTP in this scenario.
Is using ConnectionString in web.config file more secure than using in any specific aspx page?
Depends on what you do with the connection string - if you ever write it to the client, then it will never be safe! The connection string is usually placed in the configuration for reuse purposes; embedding it on every page greatly facilitates maintenance and potential errors.
And how to secure ConnectionString for highly secure website?
You can encrypt the connection - therefore it is never stored as plain text or does not use Windows authentication, so you do not need a password. This is supported by ASP.Net, as described here and here ,
source share