Parents have GC, what happens if child born outside USA?

[gcny]

Please help:

I and my wife are GreenCard Holders. My wife is currently in India, and is 2 month pregnant. Because of some medical complications, doctor has advised her against travel. This is causing lot of concerns to both me and my wife, since we had always been thinking of having the kid born in US, and hence gets automatic citizenshiop.
So, here are my questions:
- If the child is born in India, I know that he gets GC if he enters the US with the parent before his 2nd birthday. However, since the child doesnot get citizenship immediately; what rules apply to him? specifically:
1. If in the future, the child wants to come to India for studies (statring at Age 4 to 5), if he is still on Green-Card; can he come to India easily for 7-8 years to do school in India; and still maintain his GC?
2. As a green-card holder I know that I and my wife are required to abide by certain rules (e.g. live in the US, not be out of US for more than a year, etc..). Do these rules apply to the child also if he is 3-4 years old i.e. can he also not travel outside the US for more than a year at a time, etc..?
3. Does the child have to apply for re-entry permit if he were to come to India for a long duration (4-5 years) (assuming that he is still under 18 before he comes to India)?
4. What are the advantages of the child having been born in the US (and hence automatically becoming a US citizen) v/s. he being born in India (and acquiring GC upon entry with GC holder parent)?

[gcny]

****,
Thanks a lot for your reply:
Can you please throw more light on this -
1. Does your response mean that the child by himself has to maintain GC status by confirming to all the rules like living in the US; and not being away from the US for more than a year?
2. If yes, what are the options if the child wants to come here for studies starting from age 5 to age 12?
(I ask this because we have a strong desire for my child to study in India to have a good Indian culture imbibed upon him? Ofcourse for the long term, we want to have the child live with us in the US...)
3. Any other options that we have?

Thanks a lot for your reply

[Joe C]

Bring her here--all the problems will be solved. 2 months is nothing. She can take a break and come. This is the best solution.