From the contents send by you it is not clear that water leakage is from your neighbours house or from your roof.
From the contents sent by you I am in view that you are constructing a new potrtion about 45' in length. You should follow all construction procedure including laying horizontal damp proof coat with cement concrete 1;2;4 with two coats of hot bitumen and polythin sheet.For more details about dampness and water proofing you should visit the websitegharexpert.com construction section where in safety a lot of material you will find about dampness and water proofing in dampness sub section.
As you asked about old common wall, then it is necessary to know that your neighbour is also want treatment and he is ready for dismenteling and new construction then after giving both side supports you may construct new wall with DPC. Otherwise do the plaster on the wall and lay KOTA stone under the wall at the place of DPC by making cavity inthe wall in 2 to 4 feet long streches in the full width of the wall with the consent of your neighbor.