What is the difference between a web application core language and a web scripting language? What is exact use of a web scripting language like python?
Programming languages are compiled, and are usually strongly typed.
Scripting languages are interpreted, and are often weakly typed.
Python can be used for anything any other turing-complete language can be used for :)
When we use a scripting language like python with web application programming languages like Java or .net, can the web application compiler can understand the scripting language code and compile the same?
Nope. Well, there is jython, a python interpreter written in java, so in that sense, yes. But really, no.
Is it possible to write a totally new web application by using a scripting language like python?
Yeah, but python doesn't have a lot of the built-in web stuff languages like php or asp do. With a framework like Django, though, it's entirely possible to build complete, professional web applications fairly quickly (even with very little knowledge of python itself, I've found).