What is the origin of King Ravana? Is he from Sri Lanka? If so, what part of Sri Lanka does he belong to and which community are his descendants?

In Valmiki Ramayana, Sumali the Ogre had a beautiful and illustratious daughter Kaikesi. Once he saw Vaishravan Kuvera going through his aerial car Pushpak. He wanted to do good of Ogres and he told Kaikesi to go to Vishrava and marry him. Kaikesi not realising it was inauspicious time went to the Ashram of Vishrava and he was meditating. She stood in front of him all coy and shy. When he opened his eyes he found Kaikesi there and asked about her visiting him. She introduced herself and then told him to know her intentions through his meditational power. He realised her intentions through his meditation and said their union would produce terrible and fierce children because they met at inauspicious hour. She was terrified and didn't wish to have such terrible children and then he told her that their last son would be very noble and dharmic. Vishrava and Kaikesi eventually had Dashgriva, Kumbhkarna, Shurpanakha and Vibhishana. Dashgriva was later renamed Ravana because he used to make the world cry.

Source: Valmiki Ramayana

The origins of Ravana and his siblings are entirely different in Mahabharata by Ved Vyas. In Ramopakhyan, Pulastya had a son Vaishravan with his wife Gau but Vaishravan served Brahma instead of Pulastya and this angered him and he made himself into half and Vishrava was emerged. Vaishravan was King of Lanka with the grace of Mahadev and was owner of Pushpak Vimana. Seeing his father Vishrava was angry on him, he gave three Rakshasa girls as gifts to him: Pushpotaka, Raka and Malini.

Pushpotaka gave birth to Ravana and Kumbhkarna, Raka gave birth to Shurpanakha and Khar and Malini gave birth to Vibhishan.

Source- Ramopakhyan, Mahabharata, Gita Press

The Lanka in Valmiki Ramayana was in the South of Vindhyas and in Indian Ocean and most likely today’s Sri Lanka. Ram Setu also known as Adam’s Bridge is one of the strongest archeological evidences of Ramayana.

What was the origin of Vedas? How did it spread?

 Vedas are considered the "inhalations and exhalations" of Paramashiva.

Lord Shiva created Lord Brahma and then taught him the Vedas at the beginning of a kalpa (aeon), so that the process of creation can begin. This act establishes Lord Shiva as the Veda Karta (Creator of Vedas) and their ultimate origin.
To be more precise, Lord Shiva created all eighteen Vidyas (disciplines of knowledge), which include the four Vedas (Rig, Yajur, Sama, and Atharva).

There are several evidences:

~Śvetāśvatara Upaniṣad (6.18)

यो ब्रह्माणं विदधाति पूर्वं
यो वै वेदान्श्च प्रहिणोति तस्मै ।
तं ह देवमात्मबुद्धिप्रकाशं
मुमुक्षुर्वै शरणमहं प्रपद्ये ॥

Meaning:
He who created Brahmā in the beginning,
He who delivered the Vedas unto him —
That Deva (God), Śiva, who illuminates the intellect of the soul,
To Him I, seeking liberation, take refuge.

~Mahābhārata, Śānti Parva (349.65)

शिवादेव समुत्पन्ना वेदाः साङ्गा सनातनाः

Meaning:
From Śiva alone arose the eternal Vedas along with their auxiliaries.

~Liṅga Purāṇa (1.55.24)

शिववक्त्रविनिष्क्रान्ता वेदाः साङ्गाः सनातनाः

Meaning:
The eternal Vedas, along with their limbs, emerged from the mouth of Śiva.

~ Kūrma Purāṇa (1.12.129)

वेदान् सृजति देवेशः शिवो लोकमहेश्वरः

Meaning:
The Supreme Lord of the worlds, Śiva, created the Vedas.

Furthermore, It is believed that at the end of his cosmic dance (Tandava), Lord Shiva struck his drum (Damaru) 14 times. These 14 sounds formed the foundation of Sanskrit grammar and the sonic vibrations from which the Vedic hymns were realized.