Is it permissible to drop the hands to the sides during prayer, and what is the reason for some innovators striking their thighs instead of performing the Taslim?

Placing the right hand over the left in prayer is a Sunnah, not an obligation. Whoever lets their hands hang loosely and does not place their right hand over their left has missed the Sunnah, but their prayer is valid, and there is no sin upon them. As for the people of innovation (Ahl al-Bid'ah), their actions should not be paid attention to, because they do not rely on legitimate Sharia evidence; rather, they follow their whims. It is obligatory to beware of them, adhere to the Sunnah, and learn it from people of knowledge.