My fiancé is a permanent US resident but not yet a citizen, once we get married can we file form I-130 and I-485?

Best wishes for your upcoming marriage. A U.S. Lawful Permanent Resident may sponsor a spouse for immigration in the Family-based Second Preference (F2A) visa category. According to the February, 2017 Visa Bulletin issued by the U.S. Department of State, there is a visa backlog in this category (visas now are available for applicants who filed their I-130 on or before April 15, 2015), and until the Visa Bulletin shows that an applicant's Priority Date has been reached, an I-485 application for adjustment of status application cannot be filed. There is no visa backlog for spouses of U.S. citizens, who qualify for the Immediate Relative visa category. One option may be to file a Form I-130 now in the F2A category, and if your spouse becomes naturalized before your Priority Date becomes current you could request that the visa category become upgraded to Immediate Relative. There are many details that should be considered in addressing immigration application strategies, including information about your own current immigration status, and the application process often is significantly more complex than it might appear from just reading the material posted online by the USCIS and reading the immigration regulations. It would be wise for you and your fiance to consult with an immigration attorney who, after learning all of the relevant information about you and your fiance, would advise about immigration eligibilities, options and strategies and could offer legal representation in the application process (perhaps including representing your fiance in the naturalization application process to help assure that it becomes successful at the earliest possible time). Some immigration law firms, including mine, offer legal services on a "flat fee" basis so that a client will know the total expense from the very beginning, and a few immigration law firms, including mine, offer an initial consultation free of charge.

You can, but the person who is not a LPR has to be in a lawful status to adjust based on i 130 filed by the LPR.