I'm quite a newbie here, but I solved this problem by using one of the autorestart script you can find as a "sticky" post in this forum.
Not only it can run amule, but it checks whether it crashes or hangs and in that case it restarts it, keeping it running all the time :baby: . If you want this script to run everytime an user logs in (in an X environment), just put it into the /home/user/.kde/Autostart folder.
In case you use Gnome or another GUI, I guess you can find a similar folder.
Don't know about the "minimize to tray" thing, I saw some options in amule preferences, but I experienced some crashes when minimizing, so I just lost interest, after all it's not an essential feature, at least for me..

Hope this can help... Bye