The first bit to cover is the Gurudakṣiṇā or "teacher's fee". This is from the Mahabharata.
Once upon a time, the forest king had a son called Ekalavya. Ekalavya wanted to become a great warrior, so he went to go see Drona (the martial arts teacher
that pissed off that king who ended up creating a magical fire daughter that the 5 princes end up marrying and taking turns on). Anyway, he's the royal tutor so he doesn't want to teach some random Dalit to do archery and potentially be better at archery than the princes, so he tells Ekalavya no. Undeterred, Ekalavya goes back to the forest and makes a statue of Drona out of mud and pretends that Drona is teaching him, and he becomes really great at archery. One day, the 5 princes are out hunting and one of the hounds encounters Ekalavya, who shoots seven arrows into the hound's mouth, propping it open without hurting it (and stopping it barking). The eldest prince is really impressed by this display of marksmanship and finds Ekalavya and chats to him about archery. Ekalavya explains he's a disciple of Drona (he doesn't mention his "Drone" is a mud statue he pretended was teaching him). The eldest prince feels betrayed by Drona and asks him to explain. Drona chats with Ekalavya and he's really impressed by Ekalavya's dedication but ultimately is pissed there could be a Dalit archer who's better than this prince, so he says "ok if you're my disciple, prove it by cutting off your right hand's thumb". So Ekalavya does, which ruins his archery ability.
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The Mahabharata indicates that telling Ekalavya to cut off his thumb to ruin his archery was kind of a dick move, but also good on Ekalavya for knowing his place and being honourable by fulfilling the demands of his "teacher". Ekalavya later ends up being a still pretty good archer and becomes the next forest king, until he's killed by Krishna for unspecified reasons (although there's later
fanfics puranas that indicate he got killed for still being a better archer than the prince, which threatened destiny, or because he allied with Krishna's enemy).
The next one is about the worship the Aghori seem to undertake. If you're not familiar with this part of Hinduism, basically they have various sects that disagree on who the supreme God is, and most Aghori fall under Shaivism, which is that Shiva is the creator and destroyer. This gets weirdly metaphyiscal but I think it boils down to Shiva is the universe and everything in it, but can manifest into various forms in order to take part in a cosmic play. Some forms are basically Shiva incarnate (his avatars), other forms are more like creations of Shiva. Brahma (who in the original Vedic religion was the supreme God) is actually just a creation of Shiva, and while he's the "creator God" this is more in the sense of an architect rather than a supreme being.
Bhairava "the frightful one" first appears in the Tantric texts of Shaivism. These are mystical esoteric liturgical texts, the closest analogy would be something like the Gnostic gospels or the Book of Mormon (because Hinduism doesn't have a central authority so you can't really have heresies) or something like kabbalah in Judaism. They're not mainstream, they're cultic fringe texts. According to commentary this form "is the cause of crying out from fear of remaining in the cycle of suffering, and from that longing cry he becomes manifest in the radiant domain of the heart, bestowing absence of fear for those who are terrified; and because he is the Lord of those who delight in his awesome roar (bhīrava), signifying the death of Death!"
In the 9th century Netra Tantra, the Daityas (a class of asura, think titan/demigod/demon) have caused lots of issues because they keep unleashing demonic spirits of dead humans, so Shiva defeats the demigods... but now the demonic dead are all invincible because they did suffering rituals that granted them great boons, and with nobody to control them they're causing great suffering throughout the cosmos.... so he creates a manifestation of himself that's even scarier than the demonic dead. Or possibly he's Shiva's son and his brother is
king of the vampires, and it's up to Bhairava to stop the evil vampires killing everyone, except some places also worship the vampires as a manifestation of Bhairava/Shiva or just because then the vampires are on their side (there's so many different versions of these stories).
Anyway once upon a time Brahma was hanging out with the other Gods. He had 5 heads. In one version of the story, Brahma was arguing with Vishnu, and Shiva manifested as a pillar of light to break up the argument, and Brahma lied and said he'd found the top of the endless pillar of light so he won the argument with Vishnu. In another, he was actually just telling Vishnu that he was the supreme God and should be worshipped instead of Shiva. Or possibly Brahma's fifth head was really gobby and kept being arrogant/rude about Shiva. Anyway, Shiva got pissed off manifested himself as Bhairava ("the frightful one"), who then immediately beheaded Brahma's fifth head. Although Shiva himself isn't bound by any rules, Bhairava as a manifestation is. So he'd just committed the sin of killing a Brahmin (by beheading one of Brahma's heads) and discovered Brahma's head was stuck to his hand, and he'd have to atone for his sins. So he wandered around Heaven, Hell and Earth until eventually the skull fell out of his hand in the city of Varanasi. Or possibly he walked around with Brahma's head to make fun of Brahma, and got bored of carrying it and dropped it in Varanasi. Anyway, that's why the city is supposed to be very holy and important for cremations.
There's also this whole thing about Shiva being covered in ash. Basically, Hindu tradition inherited this whole thing about sacred fires and consequently the ashes from these fires also being sacred (and this is also where some of the "cow dung ash" comes into the picture). There's also an idea that as both creator and destroyer, Shiva ends up covered in the ashes of his creation. For this reason he's linked to ashes and cremation grounds, along with various other gods and goddesses
