Does anyone have a detailed map or article on the border disputes between Iran and Iraq
The only dispute I know of concerned the Shatt al-Arab. Iran claimed that the border was on the river's thalweg while Iraq claimed it was on its Iranian shore (the former was more justified IMO). Iraq dropped its claim in 1975 (the Algiers Agreement) in exchange for Iran ending its backing of Kurdish guerrillas.
and on any issues over land claims between the Mandate of Mesopatamia and Turkey
The border was disputed until a 1926 treaty between Turkey and Britain that confirmed a line drawn up by the League of Nations the previous year (the Brussels Line). The Turks wanted the former Mosul Vilayet, the British wanted a border not too different from the one that ended up being agreed on (I think they wanted Hakkari on their side of it, or at least the Assyrians petitioned them for it).
There was the Neutral Zone.
May I also ask if there is a story about where the British added Kuwait to their Iraqi Mandate as they did Zanzibar to Tangykia?
The British didn't add Zanzibar to Tanganyika, they merged to form Tanzania in 1964, after independence.