I could not get a satisfactory answer to my question on the google, they are:
To answer your questions in turn:
How secure ConnectionString is over the HttpRequest?
You should never have to pass your connection string over HTTP; what usually happens is a user makes a request, your site processes the request including connecting to the database, and returns the result to the client. Connection String should not be sent 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 out to the client then it's never going to be secure! The connection string is usually placed into config for reusability purposes; embedding it on every page makes for a lot more maintainance and potential bugs.
And how to secure ConnectionString for highly secure website?
You can encrypt the connection - so it is never stored as plain text, or use Windows Authentication so you never need a password. This is supported by ASP.Net as described here and here.