Answer 1

A website is a set of pages created using HTML/JS/PHP or similar technologies to offer info, register users and eventually allowing you to search and buy some goods, but everything is handled just with the help of your webserver, pages, a database and your browser
A web application is a piece of software you access through the browser but uses more specialized technologies.
Some application components are downloaded to your computer as plugins, other (web services) are accessed through the Internet and located in other servers and they are developed using high level languages like Python, Java, Ruby, etc.
Think about Google's main page. You can input some text to be searched (an HTML form) sent to the main database server and giving you back some listing. The control of which page are you seeing or the keywords highlighted is controlled by javascript, cookies, and PHP on the server side, but you're seeing a dynamic web site.
If you login to your Google+ account you can send mail, edit documents, spreadsheets or slideshows and the pieces of software in control of everything are complete applications you use remotely using your browser. Those are Web Apps.
As some languages and tools to create sites become more powerful, the line that separates complex websites and web applications becomes blurred.
Hope it helps.