Can the virtue of martyrdom for those who die of plague be extended to other diseases such as cancer and AIDS? What is the ruling on one who seeks refuge from the mention of cancer by spitting to his left? And where is Quba Mosque located?

A person who dies from AIDS or cancer is not considered a martyr, unless the disease was in his abdomen and he died affected by it, in which case martyrdom is hoped for him. As for seeking refuge in Allah from cancer and other diseases when they are mentioned, that is good. We know of no basis for blowing to the left.