Is it necessary to dust off a bed before sitting on it for purposes other than sleep, and is it permissible to dust it off with one's hand instead of a part of one's garment?

Shaking out the bedding is a Sunnah, and there is no sin in neglecting it. It is recommended to shake it out when one intends to sleep, not at all times. This should be done with the edge of one's garment, not with the hand, out of fear of finding a snake, scorpion, or other harmful creatures, and to avoid any harm befalling a person through their hand.