Is it permissible for a worshiper to praise Allah and mention some blessings and praise Him for them during prostration, or is only supplication prescribed therein?

Prostration is an opportune position for supplication. There is no harm in praising Allah for His blessings during prostration, but one should not go into excessive detail when enumerating these blessings, lest it become an transgression in supplication. Abundant supplication during prostration includes the encouragement to multiply requests for every need.