I'm not a Tomcat expert by far, but I'll give my 2 cents worth below. On a related note, I'd recommend checking out the Tomcat forum provided here, you'd probably get better results than here in the JSP forum.
I want to install TOMCAT on my work PC, this will open a port (local). Correct?.
Yes, Tomcat will run by default on port 8080, and accessed through the localhost.
Is this going to create any problem?. Can any one from outside the network access my PC?.
This should be fine, and only accessible by computers within your local or private network UNLESS a web server connected to your network is currently listening to port 8080 and no other applications are currently using it. Again I'm no expert, so I'd recommend checking out http://tomcat.apache.org/ for more information.