Your first question is why did the British maintain such large forces Iraq and Persia in 1942 to 1943. In addition to the answers you gave in your question, there was at least one more reason. As Wikipedia reports:
"As [the Indian 14th Army's] soon to be promoted commander Major-General William Slim wrote: 'We could move we could fight and we had begun ...
I do not think there was a lot of contact, but for what it worth, it is usually assumed that Proto-Indo-European words for "six" su̯ecs and "seven" septm were borrowed from a Semitic language.
There were other borrowings, like the Semitic word for wine, but it can more easily be explained by trade rather than direct contact.