Is it permissible to wash a hand that is in a state of major ritual impurity (janābah) with water, while there is also major ritual impurity on the garment, and then dry the hand with this garment? And after that, is it permissible to touch "al-ni'mah" (blessing/food) and pick it up from the ground, or is it necessary to wash "al-ni'mah" due to the possibility of it having touched the major ritual impurity?

The question is ambiguous. If "janabah" refers to semen that touched the hand or clothing, then it is pure according to the most authoritative opinion. However, if the hand was soiled with an impurity and then washed and dried with an impure cloth, then if the hand was wet when drying it precisely in the impure spot, it becomes impure. If one then holds something with that wet hand, the touched spot becomes impure. If the hand is dry, it does not become impure. If you are not certain that the impure spot was touched during drying, then neither the hand nor what it touched becomes impure, because impurity is not transferred by doubt. The term "janabah" is not applied to something that has been touched by impurity; rather, it has specific, known causes.