Is it permissible for a friend to request a percentage of the business profit in exchange for mortgaging his property to the bank for the purpose of Murabaha?

Your friend mortgaging his house for your sake falls under the category of suretyship and guarantee, both of which are permissible and lawful acts in Islam. The contract of guarantee is a contract of donation and benevolence, and its doer is rewarded if his intention is good. It is not permissible for the guarantor to request a fee or a percentage in exchange for his guarantee, because it is not permissible to stipulate a fee in contracts of assistance and benevolence.