If my father just passed away and left an inheritance to my sister and I but she is on Medicaid, if she declines her share of the money does it then go to me?

This depends on how the will is written.  If your sister declines her share, it is distributed as though she had died.  If the will says that the gift is divided between "you and your sister or the survivor" or that her gift lapses, then it would go to you.  If the will says that her share goes to her "and if she does not survive, to her descendants," then her money goes to her descendants.

Probably not as the government has a first lien on any heritance that occurs the moment death occurs; remember the taxpayer, that is us, is entitled to recover any expenditure we laid out for the care of your sister.