Can a Medicaid facility require a certain number of patient pay months?

Yes, here in MN many of the nicer, pricier places require that you prove you can pay for a certain amount of months (I think I saw one for 18 months). My MIL is in a nice, very reputable facility that did not require this. It is run by the Presbyterian Church. Many faith-based facilities see caring for the elderly as part of their Christian mission (I've seen NHs run by the Catholic Church, Episcopalian Church, Moravian, Lutheran and Jewish organizations). The are non-profit and so their prices are more reasonable (but not the cheapest) and their care is very good.

Yes, in some states nursing homes can require that you private pay for a certain amount of time before going on Medicaid.

I would say yes. They need to make a profit and they don't with Medicaid because Medicaid pays less than prepay. Is the facility full medicaid or only has a certain number of beds.