Answers in order:
After a dive master course, what is needed to stay cirtified?
As others have stated already, this depends on which agency you do your DM course with. As far as PADI goes, you don't need to do anything other than pay your yearly membership dues.
Do I need to pass an exam once a year to stay cirtified?
Again, I can only answer as far as PADI is concerned and thats a No.
If I teach diving, do I need to get a special insurance and who pays for it, me or the dive center?
Bear in mind that if you become a DM then the courses you can teach are pretty limited. You can not teach and certify people to dive, to do this you need to be an instructor. As a DM you can assist with this education but thats all. With regards to your question about insurance, the answer depends on where geographically you want to work. Many places in the world have minimal requirements but America & Europe for example will require insurance of varying degrees in order to operate as a professional diver. Some dive centres pay staff insurance but most require you to foot the bill.
What else do I need to know before taking this course?
I'd say you need to know what it is you want to do and what you want to achieve. If you want to work full time as a professional recreational diver then the DM cert (with few exceptions) will not be enough, you need to be looking at instructor training. If you can identify exactly what you want to do with your dive training and certifications then work back from there, that'll give you an idea of the basics you need to do straight off the bat.
if you can elaborate a little on your goal then I'll try to offer more advice