Are people inherently good according to Plato? Are Gods subject to forms, in the sense that they are good because they are subject to the form of good, or are they independent of the forms? Because I believe that since offending God in Greece is not a sin but unwise, then Gods are Gods not because they are eternal and omniscient but because they are only more powerful than us?
Are people inherently good according to Plato?
This may be a delicate question. On the one hand, Plato's Socrates asserts, in the Phaedo, concerning the misanthropist (hater of people), that only few people are genuinely good or evil.
Is it not obvious that such an one having to deal with other men, was clearly without any experience of human nature; for experience would have taught him the true state of the case, that few are the good and few the evil, and that the great majority are in the interval between them.
On the other hand, Socrates asserts in the Protagoras, that no person does evil except out of ignorance. So that no person is inherently evil:
Then, I said, no man voluntarily pursues evil, or that which he thinks to be evil. To prefer evil to good is not in human nature; and when a man is compelled to choose one of two evils, no one will choose the greater when he may have the less.
Concerning the Gods, they have been doing a lot of mischief in the Greek mythology. Socrates and Plato, however, considered this preposterous. The Gods, by them, had to be virtuous. In the Republic, Plato's programme for an ideal state includes related censorship of Homer and other poets over this issue.
Then we must not listen to Homer, or to any other poet ... And if any one asserts that the violation of oaths and treaties ... was brought about by Athene and Zeus, or that the strife and contention of the gods was instigated by Themis and Zeus, he shall not have our approval ... he must say that God did what was just and right.
If you think this relevant, In Republic II Socrates characterizes the Gods as doing only good, incapable even of making themselves 'worse' or 'less'. Gods in this way can be seen as purveyors of "The Good", the ideal form. Working off of the evidence Ram Tobolski has provided us with, Plato believes people to be similar in their attempts to do or prefer only good to evil. At the end of Republic VI, Plato includes souls into the intelligible realm of forms, placing them closer to the form of the good than physical objects. Working with this evidence, it seems like Plato would place living things among the forced of Goodness in the world. He may not say that they are solely good, or that corruption is impossible, but this could certainly translate to a 'yes' to the modern question "are people inherently good".
I'd say the evidence in Platonic texts is mixed. We have the chariot that Conifold mentions and then various images of a binding fate, as with the reincarnated souls in the Myth of Er at the end of the Republic. The dialogues are a virtual encyclopedia of contemporary viewpoints.
Generally, I believe Plato equates the Good with the Truth, so that proper education is a process of redemption. It is also a work of anamnesis or recovery, so there is a sense of Christian "fallenness" to be found in his work. Though he demonstrates in the Meno that even the slave boy is capable of recovering knowledge, and so possibly goodness as well, this contrasts somewhat with his constant appeal to guiding authority. Most people will "inherently" give rein to the bad horse.
As for the Gods, Plato's distrust of Homer and the Poets generally, was due to the awful moral examples offered by the traditional heroes and Gods. The soul needs proper guidance, whereas the poets and ancient screenwriters teach the young men of the polis to imbibe in passions and imitate the reckless antics of gunslingers.
In Socrates he dramatized a different sort of hero with a deep moral orientation in a Greek politics of ceaseless dispute, deceptive rhetoric, plague, war, and other such earthly wickedness. Were people in his view "inherently good" he might have been less firmly antidemocratic. Just look what people did to Socrates, after all!