If I configure a loopback interface and then set a router id by typing,
eigrp router-id 10.0.0.1, for example, and the router protocol is EIGRP, what will be the accurate id for this router if the ID I set is higher than the loopback address?
If you specifically set the router ID, then that is what the router ID will be.
EIGRP automatically selects an IP address to use as the router ID when an EIGRP process is started. The highest local IP address is selected and loopback interfaces are preferred. The router ID is not changed unless the EIGRP process is removed with the no router eigrp command or if the router ID is manually configured with the eigrp router-id command.