> how can I set / handle parameters like
> ?file=/link-to-my-file?
you don't.

> <http://www.mydomain.tl/home.html?file=tl_files/myfil>
> e.pdf
> 
> so that the file will not be opened in the browser
That is NOT a url or a file name. It is an argument passed to the home.html.
What the server does with it is anybody's guess.
HTT will download the url (the WHOLE url) and you get what ever that url
gives.