Internet service providers do typically keep a detailed record of which dynamic IP address is assigned to which customer at any given time. However, in general they will only give out this information to law enforcement if they receive a court order, to protect privacy.
As for MAC address, the ISP probably also knows the MAC address of the home router used at that IP address (assuming this is a residential Internet connection). However, most likely they will not know the MAC addresses of any devices behind that router, as MAC addresses are only visible within the same LAN. These MAC addresses may or may not be logged by the home router, depending on brand/configuration.