how a Roman emperor crowned?

[C Crastinus]

Didn't Domitian demand to be called "dominus et deus"?

Whether or not he actually demanded it is a matter of debate amongst scholars. Brian Jones argues that, while he didn't mind being addressed as such by flatterers, he didn't demand it of them, on the basis that there is no epigraphical evidence for it, except when he was addressed by his slaves, and the fact that he displayed great concern for observing the technicalities of the traditional religion.

Statius says that he rejected the title of Dominus. Suetonius, supported by Dio, says that he began a letter with 'Our Master and God orders' and that the habit developed from there. Only later writers (Aurelius Victor, Eutropius, and Orosius) claim that he commanded it. (Jones, 1992 pp 107-8 )