Here is how the festival was originally celebrated: On Śrāvana Pūrnima, Upākarma ritual is performed wherein Hindus change Yajñopavita. This is followed by the visit of the people of the entire village/ settlement to the house of Brāhmaṇs. Then, Brāhmaṇ tied a thread called rakṣikā to wrists of people. This thread is an oath of protection. Sons tied it to their fathers. Sisters to their brothers. Students to the teacher. Brahmans to Kshatriyas, Vaishyas & Shudras. Wife to the husband. Everyone tied rakṣikā to the king.
According to Bhaviṣya Purāṇa, Shri Krishna tells Yudhiṣṭhira everything about रक्षाबन्धन. This chapter is called रक्षाबन्धनवर्णनम्. Krishna says “Listen to me carefully as I say everything about the ceremony of Baliraksha (older name of the festival/custom).”, Krishna continues, “In the days of yore, there was a battle between Devas and Asuras. Asuras were worsted in the battle. Then asuras, with Bali as their head, reached the abode of their Guru Shukra”.
Shukra tells Asuras, “Do not despair. This is destiny. Victory & loss is bound to time. You must call a truce with Indra. For one year, Indra is invincible. This is because Shachi(wife of Indra) tied Rakshabandha to Indra. Wait for a year and you will be successful”.
Bali and Asuras couldn't defeat God Indra because of the power of Rakhi that was tied to him by his wife Shachi. Because the thread gave protection(Raksha) to Indra from Bali, its older name was “Baliraksha”. Note that as per this puranic story, Shachi actually protected Indra. So, in Rakhi, it is actually the sister who protects the brother. Through the symbolic power of the Rakhi thread.
The stories of Draupadi tying a Rakhi to Krishna or Draupadi trying a piece of cloth from her Dupatta to stop Krishna's blood flow are not from Vyasa Mahabharata. These stories have been popularized by BR Chopra's TV serial.
Alexander's wife did not tie Rakhi to King Porus. Another version of this myth says Porus' wife tied Rakhi to Alexander. There is absolutely no source, primary or secondary, for both these stories.
No, see mughals and rakhi
In 1273 CE, the Brahmins of a village named Pali tied Rakhi to the great Rajput king Rao Siha Rathore. These Brahmins from Pali village are known as Paliwals. In the same year, a Muslim army of Sultan Balban invaded the village. He died on the battlefield. Then the entire Brahmin village was killed. For this reason, the Paliwals do not celebrate Rakhi even today.