Giving Zakaat on the Pretext of Wages

Q: There is a destitute Muslim woman who is deserving of Zakaat, but feels embarrassed and does not accept it. An Aapa wishes to give her Zakaat. I shall be running a home-school next year, Insha-Allah. The Aapa suggested that I take assistance from this destitute lady in the form of student supervision, and she will give her the Zakaat and tell her that it is wages. Whereas, the Aapa and I both know that it is not wages as it is not an employment as such, and as she is very sickly, she will only come when she is well. I would like to know if the Aapa's suggestion is permissible.

Zakaat on One's House

Q: We have Alhamdullillah two houses. One we are using to live and the other we are receiving rent from it and also my father's shop is there in this house...how should we pay zakaat on it?  As far as I know there is no zakaat on the house we are living in. Please provide me with the details.