Rental income is paid out on the 5th of every month for the previous month. If the property was not rented out for that month you will not receive rent for that property.
So you are paid rent on the 5th of February for the shares that you owned during the month of January. If you invest halfway through the month you will receive rental income but only for the days that you owned the shares.
Potential Capital Appreciation Gains
When you sell your shares to another user or the house is sold after a vote you will rereceive money for your shares. It is at this point that you will realise any gains or losses made due to changes in the house price.