Hi Maggi,
Elterngeld: I have no idea. basically we wanted to apply too since it came into picture only last year but simply gave it up. i hope someone else can guide you on this. to my understanding it's more for working women who have to give up job during pregnancy... i may be wrong here!
Kindergeld: Right now my kids get 164 euro each.
Yes, irrespective of where the baby is born, if you are a resident of Germany your child will get the kindergeld. You'll to have to fill out this form (KG1) .. please check the link below:
Kindergeld - www.arbeitsagentur.de
If the baby is born in Germany then the hospital will give you original birth certificate in copies, one meant for kindergeld itself. in any case, you've to fill the form online and submit.
Latha