Question

Why does thallium form iodide only in +1 oxidation state?

Answer 1

it has nothing to do with iodide. thallium in +1 oxidation state is most stable; look up the electron configuration: [Xe] 4f14 5d10 6s2 6p1, loosing only one electron (6p1) or three (6s2 6p1) are viable options, where the former is much more thermodynamically favorable. the 6s2 is very stable and requires highly electronegative elements to get Tl+3 such as oxygen and fluorine.