What is the role of python for writing dynamic web pages? Does it play an equivalent role to php?
If so, can it do all the same things as php (MySql, file manipulation, sending emails, ...)
Looks like you don't know the most basic web development uses in Python. Some web frameworks that use Python are:

Django
Flask
Pyramid

Some of the most popular websites also use these frameworks such as Pinterest (which uses Django). EVE was made in stackless python, a form a python used on the web. In conclusion, Python is a very reliable programming language for the web along with Ruby on Rails, Dart, Hack, PHP, Perl, and JavaScript.
EDIT:
Why did I get a reputation of -2?
What is the role of python on the internet?