Yes, SN, I'll give it a go
the bible on AMS says it is unpredictable.
I have had AMS headaches and Mountaineer's Foot (can't put one in front of the other) at 8,000 ,10,000, 15,000, and 19,500 ft.... but.....plenty of time (by far most of the time) not at all. The lower altitude ones were more or less expected - only one or two days acclimatization. The worst time was at the highest even after 10 days getting that high, but heavy workload and weather contributed. The interplay is not well understood, altho complications of AMS are more common with those factors. As asked, yes illnesses can raise the risk.
Sir Edmund Hillary himself developed a high altitude stroke on Makalu in 1961. Recovered but did not go that high again. That complication is extraordinarily rare at Whitney altitudes.
The most important factor is time allowed to stage oneself higher slowly and let natural acclimatization occur. This beats Diamox. Everyone has a different pace of change, even within the same family. Only experience can tell.
Genetics are important. There are tons of studies now coming out of China. We know now for sure that some (not all) Tibetans really are superior to even other high altitude dwellers like in the Andes. We are not all created equal.
Question about iron and making hemoglobin: it is now thought that the making of extra hemoglobin over weeks of staying high is actually counterproductive. There are much better ways the body adjusts. As an example, the aforementioned superior ( to altitude) Tibetans do not have high hemoglobin levels. The other famous high altitude dwellers, Andeans, have runaway hemoglobin production and develop CMS ( Chronic Mountain Sickness) that is far different than AMS.
Bottom line - just go slow. Rule of thumb is advancing sleeping altitude 1,000 ft per day above 10,000 ft, some would say 7-8,000 ft where the actual definition of AMS begins.
Hope this lengthy reply helps.
