The new place does not sound like a good option if it's in the process of being sold in foreclosure. Generally a buyer out of foreclosure will take "subject to" an existing lease, but that would still leave you with a great deal of uncertainty abut who your landlord is.
As for your current place, the mediation certificate *PROBABLY* indicates that mediation has been successfully concluded and an agreement has been reached between your current landlord and her lender. You will need to go down to the county recorder's office and get a copy of the document to know for sure. Even if mediation has resulted in some kind of workout between the owner and the lender, a new foreclosure action could still be initiated down the road if the owner defaults on the new deal.
Also note that the document could be certificate issued to the lender in response to a request for a finding that mediation is not required because the homeowner waived mediation or failed to elect to mediate after being advised of the right to do so. Again, that's why it's really important to go to the recorder's office and find out what the actual recorded document is.