Can I get different outputs from the xml-file using the browser?

Check the relevant documentation for your browser. The most likely
outcome is that you have to use some browser specific scripting.

How would I define the xslt file if that is not hardcoded in the xml-file?

How do you want to tell the browser which XSLT file to use? Again,
this most probably involves browser specific scripting too.

You might get help for the task if you tell us what browser you use,
but you'll probably get faster and better help on a browser specific
list.