If my wife is here legally with her stay ending in a month and a half, which forms do I need to file for her green card and does she have to go back?

More information is needed in order to provide an immigration legal analysis and to answer your questions. Note, however, that generally if a foreign national entered the U.S. lawfully and with inspection (such as with a temporary visa) and becomes married to a U.S. citizen, the couple can succeed with a marriage-based adjustment of status application without the foreign national needing to return abroad; this is true even if the foreign national spouse may have overstayed an initial visa. It would be wise for you and your wife to consult with an immigration attorney who, after learning all of the relevant information about you, your wife, your wife's immigration-related history, etc., would be able to advise about immigration eligibilities, options and strategies, and then would be able to offer legal representation in the often quite complex application process.