Can my partner obtain citizenship if we were to get married?

No, same sex marriage is not recognized by federal laws and immigration is federal law. It does not matter if you get married in a state that recognizes gay marriage. It will not allow him to derive any immigration benefits from you. He can apply for permanent residence on the basis of employment, however, once he finishes his studies and gets a job.

This is a difficult question at this time. The best answer may be almost, but not quite. The recognition of same-sex marriages under federal immigration laws is currently being litigated. You may have some options, but it will not be as clear as it should be what your best course of action will be.

Not under current law.

Unfortunately, Federal Immigration law does not recognize same sex marriages at this time. Therefore you cannot sponsor your same-sex partner. You should petition your congress person regarding this issue.

In my personal opinion, you should be able to file an immigrant petition for him and get it approved. Your spouse would not become a citizen overnight, of course, he would file for adjustment of status to a Lawful Permanent Resident ("green card") first, and then for citizenship 3 years later. A professional opinion must differ. Previously, federal Defense of Marriage Act stood as a bar to recognition of same-sex marriages by the Immigration Service (and all other federal agencies). A couple of years ago, a lower federal court declared the DOMA unconstitutional. Obama administration very loudly announced that it will not appeal the decision (and get DOMA out of the way). GLBT community and libertarians applauded the President for his commitment to equality of all under the law. It turned out, however, that the administration changed its mind and, not so loudly, appealed to the Supreme Court. In fairness, it must be said that the President might be trying to get DOMA struck down by the Supreme Court - just in case another man will ascend to the presidency and revive this deeply bigoted law. My willingness to give Mr. President the benefit of the doubt is, however, undermined by his instruction to the federal agencies to continue enforcing DOMA until the Supreme Court hand down its decision (which is not likely to happen until next summer). The President not only did not have to do that - his instruction is, arguably, unlawful because the decisions of the lower courts declaring DOMA unconstitutional should render it unenforceable. But... Democrats are not likely to challenge anything the President decides, and the Republicans are not likely to push the President to start granting immigration benefits to same-sex spouses of U.S. citizens. So, right now, you have to wait for the Supreme Court of the United States to decide whether the Constitution gives gay Americans the same rights as to their straight brethren.

No. However, how old is now and how old is he when he entered.

Not likely under current interpretations, but might be able to get a work permit.