If I have financial guardianship of the estate, can I buy my Mom's house?

It depends. Consult a elder care lawyer familiar with Medicaid planning, especially if she is in nursing home on Medicaid. Home may have a lien due to Medicaid, or the sale of home may disqualify your mother for Medicaid in the month she receives funds. You have guardianship so you are held to reporting and ethical standards by the courts. Be cautious.

I think legally probably yes, but ethically you are in essence making a contract with yourself so it is a little stickier. You would need find a way to set it up in a way that is above reproach, perhaps through some kind of third party..