1. You have to be a US citizen to sponsor her Green card. For Green Card holders as I recall the only family other than the children and wife they can sponsor is unmarried adult children over 21 but unmarried you can apply for their Green Card. Once you become US citizen your possible beneficiaries can be larger including your parents. There is little-known provision that is sometimes used, use it if it's necessary when let say your parents they don't have anybody in India to take care of them.

Watch the Video on this FAQ: What are Visa Bulletin Final Action Dates and Date for Filing

Video Transcript: 

Pay your taxes, don't default on your taxes, try not to get too many traffic tickets. If you get few that's OK, but if you get too many that can be ground for troubles. Don't get into any criminal plot, as you can lose your Green Card if you have a felony conviction. There are other things that can hurt your Green Card like DUI more than one or two of them then you can get into trouble. So, as long as you are like regular people I don't think there is anything to worry about.

1. There is no such requirement that I am aware of at this point today (June 2017) that you have to notify any US government agency or Indian government just because you received your Green Card. However, what you should do is you should inform your employer that you have got your Green Card so they can update your Form I-9 which is an internal matter within the files of the employer. They don't have to update any government agencies.