Will I inherit his other debt if I get executive order estate?

If you inherit property subject to a security interest, like a mortgage, that property can be used to pay the debt, but you are not personally liable. Since the mortgage on the house is already in arrears it is unlikely that you can stop the foreclosure action by merely paying off the arrearage. You will have to refinance the entire mortgage. This will require the estate to distribute the property to you. If you receive other assets from the estate, assets that could have been liquidated and used to pay creditors of the estate, then those creditors can follow the assets and seek to have the assets turned over or they could attach and sell the assets to pay the estate debt. You would not be personally liable for the estate debts but you cannot receive an estate distribution if the estate owes money to creditors.