Although some states might allow Medicaid, probably private pay plan until she has a Green Card. Then she will qualify for Obama Care. Mom will not be eligible for Medicare until she is 65 and either has been a Green Card holder for 5 years or is a US citizen. At that point, since she will not have been working for 10 years, she will have to buy into Medicare Parts A&B.
If she marries a US citizen, things will be different regarding Social Security benefits (age 62) and Medicare (age 65).