I want to know who has written our Puranas? Where in our scriptures, is it mentioned about the author? Are the Puranas created and composed ('put together out of existing material') by the same person(s)?
According to Matysa Purana, Lord Brahma composed Puranas for the first time. Chapter 3 Primary Creation of Matsya Purana says
Before the creation of all the 'sästras, Brahmä composed the Puränas, which happen to be indestructible, full of words, auspicious and were comprised of a hundred crores of the verses.
Thereafter, there emerged from the mouth of Brahmä, the Vedas with their accessories, mimctmsä and nyäya. Thereafter the sons of Brahmä, who were engaged in the recitation of the Vedas, were born with the desire of his mind. Because they were born of the mental desire of Brahmä, they came to be known as the mind-born sons of Brahmä.
This is described in detail in Chapter 53 of Matsya Purana.
Lord Matsya (Vishnu) said to Manu, "Brahmä remembered in the beginning first the Puränas among all the Sästras. So Puränas are the first among the Sästras. Afterwards, Brahmä uttered out the four Vedas from His four mouths. There was only one Puräna in the beginning of the Kalpa. It was alone the means of the accomplishment of the three ends of man (Dharma, Artha and Käma). And it was the only holy book consisting of thousand millions of stanzas.
When all the regions perished by fire at the Great Dissolution, then I recited the four Vedas, with their six Angas as well as the Puräpas, the manifold Nyäyas, the Mimämsä and the Dharmasästra. In the beginning of the new age, immersed myself in the furious waters, at the time of dissolution of the universe and explained them fully to Brahmä, Who in His turn revealed them to the Devas and the sages, after which they spread all over the world. Therefore, the Puränas became the source of all other Sästras. Later on, seeing the neglect of the Purana under the changed circumstances, I repromulgated them in every yuga, through my partial incarnation of Vyäsa. In every Dväpara yuga, I compiled the Puränas to the extent of four lacs of slokas, and spread them in the world after dividing them into eighteen. Even now the bulk of the Puräna extends to a hundred crore verses in the Deva loka. On the universe, however, its bulk is abridged only to 4 lakhs of 'lokas, and is divided into eighteen Puränas".
I googled and I got this:
अष्टादशपुराणानां सारं व्यासेन कीर्तितम् | परोपकार: पुण्याय पापाय परपीडनम् ||
हिंदी अनुवाद: कीर्तिस्वरूप अठारह पुराणों के सार के रूप में महर्षि व्यास ने सिर्फ दो बातें कहीं !! दूसरो का उपकार करने से पुण्य होता है और दुःख देने से पाप । एक प्रचलित कहावत भी है -परहित सरिस धरम नहि भाई, परपीड़ा सम नहि अधिकाई ।
English Translation: Amidst all the 18 Puranas, know only two gospels of Maharshi Vyas to be true, that doing good to others conduces to merit and doing harm to them leads to Sin.
So Maharshi Vyasa wrote the Puranas according to above shloka. But I didn't find which of our scriptures mention this shloka.
Vyāsa (Kṛṣṇa Dvaipāyana) authored the "master Purāṇa" called Purāṇasaṃhitā — a collection of stories, songs and sayings — which he passed down to his disciple Romaharṣaṇa who in turn taught them to his disciples (Kāśyapa, Sāvarṇi and Śāṃsapāyana) and they created their own versions of the original saṃhitā. From these saṃhitās arose the first few Mahā-purāṇas (main purāṇas) but no one knows exactly who authored them and when. But this process of creating purāṇas from the various purāṇasaṃhitās continued for several centuries until the number of Mahā-purāṇas and Upa-purāṇas (minor) settled at 18 each by A.D. 700.
Evolution of the Purāṇas
Though it is conceded that the purāṇas are of hoary antiquity, extreme paucity of information leaves us in complete darkness with regard to their character or contents, none of which seems to have come down to us in the original form. No doubt Hindu tradition attributes the authorship of these purāṇas — the eighteen Mahāpurāṇas (the main purāṇas) and the eighteen Upapurāṇas (the subsidiary purāṇas)— to the sage Kṛṣṇa Dvaipāyana, better known as Vedavyāsa or Vyāsa.
However, this cannot be substantiated by the evidence available. The original purāṇa referred to in the Vedic and allied literature was, perhaps, a conglomeration of ākhyānas (tales), upākhyānas (anecdotes), gāthās (metrical songs or proverbial sayings current in the ancient society) and Kalpakoṭis (sayings that had come down through the ages). The sage Vedavyāsa might have compiled these into one Purāṇasaṃhitā. His disciples and their disciples as also others in that tradition might have composed more detailed works which gradually took the present form, the eighteen purāṇas as we know them today. This surmise is confirmed by the accounts given in some of the more ancient purāṇas like the Vāyupurāṇa, the Brahmāṇḍapurāṇa and the Viṣṇupurāṇa. According to them, after compiling the original Purāṇasaṃhitā, Vyāsa imparted it to his disciple Sūta Romaharṣaṇa (also spelt as Lomaharṣaṇa), who in his turn made it into six versions and taught them to his six disciples. Of these, three disciples viz., Kāśyapa, Sāvarṇi and Śāṃsapāyana made three separate saṃhitās which were named after them. These three, along with that of Romaharṣaṇa are known as 'mūlasaṃhitās'. The later purāṇas were evolved out of these.
Growth of the Present Mahāpurāṇas
When exactly the original purāṇic material began to give rise to different purāṇasaṃhitās, it is difficult to say. Since the Taittirīya Āraṇyaka as also the law books of Manu and Yājñavalkya have used the word 'purāṇani' (the 'purāṇas,' in plural number) it cannot be denied that three or more purāṇas had come into existence long before the beginning of the Christian era. By the time of Āpastamba (450-350 B.C.) the term 'purāṇa' had already become restricted to designate a particular class of books. It is not known how many purāṇas existed during Āpastamba's time and how they went on growing in number. But we do find a tradition recorded in almost all the extant purāṇas and other allied works, that the purāṇas, or rather the Mahāpurāṇas, are eighteen in number. The names of these eighteen purāṇas as given in different purāṇic works, are more or less the same as those of the works now extant under the general title 'Mahāpurāṇa'. Based on the evidence of the Matsya and the Kūrma purāṇas as also some other Sanskrit works, we can safely assume that by AD. 700, the evolution into eighteen Mahāpurāṇas had become complete and the number got rigidly fixed there.