Does placing a prayer jilbab over a cover that touched a dry menstruation bloodstain make it impure and prevent praying in it? And does the splashing of water used for istinja' (ablution after defecation/urination) on the arm, and then on the shirt, make the shirt impure and necessitate repeating the prayer?

Dry impurity does not transfer to dry objects that it touches, and the hand is not judged impure merely by being splashed with water. The original ruling concerning water droplets that splash during istinja' (washing after relieving oneself) is purity. The questioner should desist from obsessive doubts and strive against her soul to repel them, clinging to the fundamental principle, which is the purity of things.