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. We have been able to extend their tourist visa in those cases, stay in tourist visa even though you are on Green card we can try to make an argument that there is nobody in India to take care of them. This provision is not very clear cut in cases of holders of Green Card but believe it or not if you are on non-immigrant visa like student or H-1 visa or O-1 or B-1 any of those visas or L-1, you actually have more rights to bring your parents here. The reason being that there are certain categories of visas where people are not directly dependent and you cannot sponsor them for derivative visas but government recognizes that we will give you an extension of tourist visas. So if you are here on H-1 and you wanted to bring your mother here because she is alone in India, you could actually do her because she can't get her H-4 being your mother, she can still get B-1 or B-2 which can be extended because she is recognized or covered under those situations. However, Green card holders they don't have same privilege but you can be able to get their extension sometimes. It's not the full proof method for me wait until you get naturalization. Once you are naturalized, your parents can be here within a year on a Green Card.
2. I have done it repeatedly, every six months we have to do it, there are some people who are in 3rd, 4th or 5th year we are doing repeatedly for them. But it's not or no means it should be taken as given or guaranteed rule.