Can she still keep the house...Exactly what law governs that..Also can she start receiving his social security benefits..Exactly what law governs that

Illinois law governs the house.  Whether or not your mother can keep it requires the answers to several more questions.  I urge you to contact an attorney in Alton experienced in real estate matters. As to Social Security, that also requires more information to determine.  I suggest that you try the Social Security Administration's web sit at www.ssa.gov.  You can get answers to questions and apply for benefits there.