Answer 1

A cookie isn't specific to c#. ASP.net web applications work with cookies because they're part of the HTTP protocol and an important part of how websites and web applications in general work. Like PHP and many other web development languages or tools, ASP.net lets you access what cookies were passed to the server and lets you modify the cookies sent back to the browser.
A cookie is basically a key and value pair that gets passed back and forth between the web browser and the web server. It can persist in the web browser similar to local storage. It is often used to identify session for a logged in user on a website but can be used to track lots of other small pieces of information.