I'm not a student of philosophy or mythology, so please keep what you say simple and explanatory.
I see most of the Greek mythology is based on Hesiod's work Theogony as is evident from the current historical records. What really motivated Hesiod to write such a work? Did he or anyone else, such as Homer, ever claimed that they were divinely inspired or any such thing?
I think once I read that the persons who wrote Hindu mythology were divinely inspired. What was the status of Greek mythology in Greek culture and society? Was it taken as a religion, a time pass activity, or a part of literature of that time?
Hindu mythology is, you can say, seen as a religion by Hindus. I observe there is a kind of similarity between cosmogonic claims of both Greek and Hindu mythologies. What are the reasons for this?
They both assume the universe started from nothing. When Romans invaded Greece, they stole the ideas of Greek mythology, such as concepts of gods, to make part of their own culture. Did Romans have no mythology of their own, if they did, then what aspects of Greek mythology fascinated them to such a degree that they incorporated most of it?
The classical mythology is a system of mythology of the Greeks and Romans together; much of Roman mythology (especially the gods) was borrowed from the Greeks. Graeco-Roman deity, Greco-Roman deity is a deity of classical mythology.
In the table of Greek gods under link No. 1, at first sight you are misled into believing that Thaumas, along with others under the same tree (on the far top left), was a son of Oceanus and Gaia. In fact, his and others' parents were Pontus and Gaia. Did the layout also give you the same wrong impression?
Thank you for reading this, your time, and any help you could offer.