an Apache server on my PC (localhost) ?

[kevin001]

Dose Apache works exactly like an online server ? Can I set a cookie on an apache server? Dose Apache suppot php, MySql, AJAX, XML etc. Actually WHAT is the differene, if any, between a web host on the internet and an Apache server on my PC (localhost) ?

[Altrea]

Dose Apache works exactly like an online server ?

Not clearly answerable.
following i assume by "Apache" you mean "Apache HTTPD" and not "Apache Tomcat" or another Apache project.

Can I set a cookie on an apache server?

You can set Cookies with Apache HTTPD module mod_headers
But i believe that is not what you want to do.

Dose Apache suppot php [...]

Apache HTTPD supports to implement an PHP interpreter. It can not natively parse php code.

[...] MySql [...]

rudimentary with mod_dbd
But i believe that is not what you want to do

[...] AJAX [...]

AJAX doesn't make sense without a serverside running programming language, so natively: no.

XML

XML is just a plain text format. Apache HTTPD can output all plain text formats like HTML, XML, txt, YAML, etc. But the magic behind this have to be done by a serverside programming language or clients browser.

Actually WHAT is the differene, if any, between a web host on the internet and an Apache server on my PC (localhost) ?

The difference between what?
The better question would be: What is a HTTP daemon (HTTPD).
A HTTP Daemon is a HTTP (HTTP is a transfer protocol for hypertext - e.g. html) compliant webserver that listens for requests to response.

More informations on that:
http://wiki.apache.org/httpd/FAQ
http://en.wikipedia.org/wiki/Apache_HTTPD

btw: localhost is just a named alias hostname for for your very own computer, routed by your loopback network interface.

if you ask me, you should now take some time to learn the basics. That is very important to understand what you want and what you need for that.