How do I add something new to the Menu Bar, or whatever it is called?

By Menu Bar, I mean that which contains Portal Page, Forum List, My Stuff, etc.

What php file is it, and where is it located?

I had it figured out in 6.5.5

I haven't yet figured it out for version 7.

You're looking for the header.tpl template file. If you've set the permissions on your templates to be writeable you can edit this in the control panel in the Templates section. Otherwise you'll need to edit the file via ftp. templates/default/header.tpl

Is there an example available how to enter another drop down menu in header.tpl? I like to ada an 'extra' meneu entry who contains all what I add to the board such as chat and gallery for example.

Thank you.

How can I remove one without actually deleting it from the file itself, as I may wish to use it again in the future?

You can comment it out using

<!--
text or code
-->

Thank you.