Does the prayer become invalid due to the forehead moving during prostration as a result of uttering the dhikr or a slight slip on the mosque's carpet?

We ask God to grant you well-being and guidance. The whispers (waswas) have greatly affected you because you have indulged them. The only cure for them is to ignore them and not pay them any mind. Your prayer is valid, and beware of responding to Satan's whispers by repeating it. You are not required to freeze your head in prostration; rather, what is obligatory is to place the head on the ground, and its slipping due to the carpet does not harm.