Does websites like twitter and facebook ( where the content change often ) use caching ?
Yes, these sites heavily rely on (different type of) caching. They likely using special solutions that extremely fine-tuned to fit their needs because every kind of web applications has their weakness.
High Scalability has great articles in this topic.
Yes. A commonly used cache software is memcached
You should read up on caching and how it works and how it does not. Here is a link to a very large cache tutorial/faq
Look at this article:
http://royal.pingdom.com/2010/06/18/the-software-behind-facebook/
Memcached is by now one of the most famous pieces of software on the internet. It’s a distributed memory caching system which Facebook (and a ton of other sites) use as a caching layer between the web servers and MySQL servers (since database access is relatively slow). Through the years, Facebook has made a ton of optimizations to Memcached and the surrounding software (like optimizing the network stack).