Thinking about Roman or even just pre-christian paganism in the terms we think about Christianity today or even as it was thought of by the reign of Theodosius, who made Christianity the official religion of he empire, can have us running into some anachronistic problems. Roman paganism did not have much of any form of heresy. The closest thing I can think of is people practising personal magic in addition to state cult, magic being socially frowned upon as it was considered to be much more nefarious in nature. But the big thing to understand about Roman paganism is that it was very tied into civil society. Romans didn't really care which gods you chose to worship as long as they were those worshipped by everyone else. The other big point, a classic point regarding ancient Roman practices in general, is they were masters of appropriating other cultures and systems and integrating them into the empire. Thus the comparisons between various classical heroes and gods and those from other cultures like the Near East. Worshipping the god of Tyre would have been equated to worshipping the closest similar Roman deity or hero, such as Hercules. Even when Christians were persecuted it was not because they worshipped the wrong or different god, but because they refused to sacrifice as ALL pagans and traditional religionists had. We get to notions of heresy much more as it relates to the Christian faith. Persecutions led to infighting between Christians, as some challenged others for forsaking the faith in order to live rather than die a martyr. Then when Christianity gained more significance during he reign of Constantine we find a variety of heresies within the faith because Christianity did represent a fundamental break with paganism. It was no longer a go with the flow kind of religion, but a universal, Orthodox one, whose correct worship affected all humans, and thus it was considered important that all Christians worship correctly, hence Orthodox.

A great book on this topic is Pagans and Christians by Robin Lane Fox. Also consider looking at Peter Brown's The World of Late Antiquity.

Neither, really. The popular understanding of Greco-Roman mythology comes from a variety of elite literary sources that were not actually representative of what the author actually believed, but were treated in much the same way that "folk tales" are today. And really, if you read a given account of a Greek myth there is a very strong possibility that the source was a single work, the Metamorphoses by Ovid. To give one of my favorite examples of this, the Iliad is arguably the most famous work of classical antiquity and almost certainly the most literately significant, but if you think of the primary character, Achilles, the first thing that usually pops into mind would be his heel, the one part of his body that was vulnerable. But the heel is not mentioned in Homer, and there is no suggestion in the Iliad that Achilles has such invulnerability, but the heel does appear in Ovid.

But Ovid was not really being sincere, his work is unapologetically literary, filled with ironic self reference and self parody. What Ovid's actual beliefs were is of course inaccessible, but the Metamorphoses was undoubtedly not meant to be taken seriously as history. It instead belonged to the category of what the great Roman scholar Varro called "the religion of the poets", the sort of thing that only the most ignorant bumpkin believes but makes a good story (Varro's critique of mythology follows in a long tradition, back to the Archaic poet Xenophones, but that is another story). This is contrasted first to the religion of the cities, the mix and match of ritual that held the community fabric together. The last as the religion of the philosophers.

So does this mean that the mythology we have is an accurate representation of "common folk" belief? Well, not quite. The mythology we have is a highly learned one stemming from the great works of Alexandrian compilation, and doesn't necessarily reflect what anyone ever actually believed. For example, while there is one "canonical version" of the story of Echo and Narcissus, there are a couple other ones mentioned in passing, for example, the author Pausanias mentions that in one area of Greece, Narcissus is not said to have fallen in love with his reflection, but with his twin brother. More substantively that divergence in myth, however, is that myth as we know it only barely touches on actual observable ritual practice. The many different Etruscan methods of divination, for example, continue all the way through Late Antiquity. Among Latin Romans, the focus of religious activity weren't the gods, but rather the ancestral spirits. And if you go outside of Attic Greece or Latin Rome any idea of "normal" goes out the window, as local and international traditions blend together.