Let us assume that you are the system admin of a linux server which
runs as a web server hosting html and php websites. Let us also assume
that this server also runs as an email server and mysql database server.
Let us assume that you manage the server from a remote location using
ssh. Suppose if an user calls you over telephone and says that the sites
are very slow, how will you approach the problem. Describe the questions
you will ask the user and then explain all the checks you will make
before you identify the culprit process. Before checking the server,
what are the different problems you envison? How will you check each of
these potential problems.

If you're asking what to look for when switching hosts to a faster box - the biggest issue you'll deal with will most likely be version inconsistencies between hosts. If Host A is running an older version of SQL/MySQL/PHP than the server you're moving to at Host B, you're apt to run into some problems.

This isn't really a security question.
It also reads a lot like you're asking us to do homework questions for you.

Please, no homework and no cross-posting..