You can run
to edit your cronjobs. There you enter
*/15 * * * * wget -O - --http-user=username --http-passwd=password "https://dynamic.zoneedit.com/auth/dynamic.html?host=domain.com"
and save the file.
Should I run this job as root?
At least you won't have any permissions problem then...
If you know the cron job is working and doesn't destroy anything, then you can run it as root.
What if I need to update 3 other domains? Do I create 3 other cron jobs?