Is it necessary for my spouse to be physically present in United States for me to make her an American citizen?

She cannot just become a US citizen because she is married to you, whether you are in the US or abroad. You first have to petition for her permanent residence and only once she gets that and is a permanent resident for 3 years can she apply for US citizenship. Please let me know if you have any additional questions or how I can be of further assistance to you in this matter.

First she needs to get a green card and then she can apply for citizenship.

Your wife cannot automatically become a U.S. citizen, just because she is married to a U.S. citizen. You must petition her for a green card first and then 3 years after she has had a green card, she can file for naturalization. I suggest that you contact an experienced immigration attorney for a face-to-face consultation and give him/her all of the facts surrounding your situation. He/she would then be in a better position to analyze your case, advise you of your options and, if possible, make sure that the necessary paperwork and documentation is presented so as not to delay the process.

As an American citizen currently studying abroad, but domiciled in the U.S., you are able to sponsor your foreign national spouse. The earliest your spouse will qualify for U.S. citizenship will be 2 years and 9 months after she becomes a permanent resident, by showing that she (1) is married to you for at least 3 years; (2) continues to reside with you in a marital union; (3) is physically present in the U.S. for at least 18 months (in aggregate), (4) not taking any one trip lasting 6 or more months (this creates a presumption that she abandoned her residence, and although she will be allowed to present evidence to rebut this presumption, to keep it simple, she should keep her absences for ); (5) is a resident of the state or district from which she applies for at least 3 months. Also note that if at the time your spouse is admitted for permanent residency she is married to you less than 2 years, she will only be granted a 2-year conditional residency. Thus, before she can apply for U.S. citizenship, and within 90 days leading to the expiration of her 2-year green card, the two of you would file Form I-751 to remove the condition and obtain her permanent, unconditional residency (10-year green card). Hopefully this information helps.

No that is not possible.

Your alien spouse must first acquire a green card. After s/he becomes a green card holder and assuming you remain married for 3 years after that, your spouse may then apply for US citizenship. One of the requirements for US citizenship is physical presence in the US. Depending on where and why you are presently stationed overseas, DHS may waive the physical presence requirements necessary for naturalization. You will need to speak to an attorney to advise you further.