Is there any harm in resting the hands on the hips while sitting and clasping them behind the back while walking, and how accurate is the belief that these actions indicate arrogance?

Placing the hands on the hips or behind the back is not forbidden, except that the prohibition of placing the hand on the hip is specifically in prayer only, based on the saying of Abu Hurayrah: "He ﷺ forbade a man from praying with his hand on his hip (mutakhassiran)." As for placing the hands behind the back, there is no harm in it, unless it leads to arrogance, in which case it is forbidden due to the prohibition of pride. The Prophet ﷺ said: "No one who has the weight of a mustard seed of pride in his heart will enter Paradise."