You're correct, the info file is the link next to the extension name on the download page. The dep file does not have a link, but if you're interested you can see it by substituting .dep for .info in the url for the info file.
Maybe it would be better to download and manually load an extension from a terminal window to check if there are any error messages.
I don't use minefield, but according to the dep file, it depends on the following extensions:
expat2.tcel
glib2.tcel
graphics-libs-1.tcel
libxml2.tcel
fontconfig.tcel
gtk+-2.tcel
If you download these one by one and store them somewhere permanent, you can load them individually as follows from a terminal window: $ tce-load /path-to-file/expat2.tcel
$ tce-load /path-to-file/glib2.tcel
...
$ tce-load /path-to-file/gtk+-2.tcel
$ tce-load /path-to-file/minefield.tce
This way you'll see any error messages in the terminal window and hopefully get to the bottom of the problem. If everything goes well, you should be able to launch firefox from the icon at the bottom of the screen.