Hi all.
My configuration: Joomla 1.0.15 + Joomfish 1.8.2 + Artio 2.3.0

Everything goes well but root link (Home) in pathway navigation chain:

Home->Section1

Child links are in the following format: www.mysite.com/en/section1/
But the root link anyway remains like www.mysite.com/index.php?lang=en
That's interesting, but the same item Home in the Mainmenu module changes right way and looks like this: www.mysite.com/en

How can I remove duplicate link www.mysite.com/index.php?lang=en and change it for www.mysite.com/en ?

This may be caused by the module that is used to generate the links in question (to make the links SEF, they need to be parsed via sefRelToAbs function in Joomla 1.0.x and using JRouter in Joomla 1.5.x).

To remove the index.php you may change the JoomSEF configuration - default index file. You may also leave it empty.