Is it possible to run django without shell access? My hoster supports the following for 5€/month:
There is no shell nor cronjob support, which costs additional 10€/month, so I'm trying to avoid it.
I know that Google Apps also work without shell access, but I assume that is possible because of their special configuration.
It is possible.
Usually you will develop your application locally (where shell access is nice to have) and publish your work to your server. All you need for this is FTP access and some way to import a database dump from your development database (often hosters provide an installation of phpMyAdmin for this).
python (I assume via mod_python)
From my experience, you are most certainly wrong with that assumption. Many low-cost providers claim to support python but in fact provide only an outdated version that can be used with CGI scripts. This setup will have a pretty low performance for Django apps.
It's possible but not desirable. Having shell access makes it possible to centralise things properly using symlinks.
Get a better host would be my first suggestion. WebFaction is the most recommended shared host for using with Django.
If that's out of your price range, there are plenty of hosts that give you a proper system account (vs just a ftp account) and have mod_python or mod_wsgi (preferred now).
Google Apps works without shell because their system looks for a dispatcher script that you have to write to an exact specification.