I am asking about the original Parashara - not the Srivaishnavite teacher Parasara Bhattar.
Which works are attributed to him?
Veda Vyasa, the compiler of the Vedas, the author of the various Puranas and Mahabharata, is a son of Parashara Rishi and Satyavati.
Even before the birth of Parāśara, Kalmāṣapāda in his demoniacal form ate his father, Śakti. Therefore Parāśara nurtured an obstinate hatred against the Rākṣasas. So he performed a Yāga to kill all the rākṣasas. Thousands of rākṣasas were burnt to death at this yāga and Vasiṣṭha, grandfather of Parāśara felt sorry for the innocent rākṣasas. He approached Parāśara and said "Son, do not give way to such anger. Abandon this wrath. What harm have these poor rākṣasas done? Death was in the destiny of your father. Every one has to suffer the result of his own deeds. Anger destroys the fame and austerity which one has attained by years of toil. Therefore abandon your anger and wind up your Yāga."
Parāśara accepted the abvice of his grandfather. Vasiṣṭha was pleased with his grandson and at that time Pulastyamaharṣi son of Brahmā also came there. Vasiṣṭha gave arghya (water and flowers) and received him. Then Vasiṣṭha and Pulastya jointly blessed him and said he would be the author of Purāṇasaṃhitā. Thus Parāśara became the best of the Guruparamparā (traditional line of preceptors). (Chapter 1, Aṃśa 1, Viṣṇu Purāṇa).
Birth of Vyāsa.
Parāśara begot a son of a fisherwoman named Satyavatī and the boy became later the celebrated Vyāsa.
He was the composer of the Vishnu Purana, the Parshara Smriti and also the astrological treatise called "Brihat Parashara Hora Shastra".
The Bṛhat Parāśara Horāśāstra is the most comprehensive extant work on natal astrology in Hindu astrology ascribed to any Rishi or sage according to the text itself. Its oldest printed version is a composite work of 71 chapters, in which the first part (chapters 1-51) dates to the 7th and early 8th centuries, and the second part (chapters 52-71) dates to the latter part of the 8th century.
The text says that this work was created by Sage Parāśara, father of Vedavyāsa who was the compiler of the Epic Mahabharata for the benefit of Kaliyuga.
The Visnu Purana as herein recorded was spoken by Parasara Muni to the sage Maitreya. Parasara Muni is the father of Krsna Dvaipayana Vyasa, the compiler of the Vedas and author of Mahabharata. In Mahabharata, the story of Vyasa’s birth is told. Once, Parasara Muni desired to cross the river and the boatman had engaged his beautiful daughter, Satyavati, to ply the boat that day. Parasara became enamored with Satyavati’s beauty1 and while halfway across the wide river, he expressed his desire for intimate relations with her.
And, regarding the Parashara Smriti, the first chapter of the text makes it clear that the law-giver (or the author of the scripture) here is Parashara Rishi.
When several Rishis asked Vyasa to expound the laws, he says it was not possible for him to do that. Instead he recommended asking his father (i.e. Parashara). This is how the text begins.
Now to begin. — On the top of the snowy hill, in the hermitage of the Devadaru grove, the Rishis of yore interrogated Vyasa, who was seated, rapt in thought.
Expound, O son of Satyavati ! the law, which is for the good of mankind, in the present Kali age; and the practice of purification, such as it ought to be.
Hearing the above saying of the Rishis, (he) the adept in the Veda and the Smriti, and exceedingly bright, like a a kindled fire or the sun, who was attended by his pupils, said in reply,
" I have not the knowledge of the whole of the truth. How can I venture to expound the law ? It is our father who should be asked." Thus said Vyasa, the son.
6, 7. Then all those Rishis, desirous to obtain correct law, proceeded, under the lead of the Rishi Vyasa, to the Badrika hermitage, (a spot) crowded with various trees, beautified by flowers and fruits, diversified by rivers and rills, ornamented with holy bathing-places, resonant with the voice of beasts and birds, studded with temples, and enlivened by the dance and music of Yakshas, Gandharvas and Siddas
8 & 9. There, Vyasa, accompanied by the Rishis, by putting together both his palms and by cir cum ambulation, obeisances and laudatory speeches, paid respects to Parasara, the son of Shakti, seated at his ease in the midst of an assemblage of Rishis, and surrounded by a host of Munis of the highest rank.
- Now, with a gladdened heart, the great Muni Parasara, pre-eminent among Munis, thus spoke without rising from his seat, " Tell(me) about your safe arrival."
Some other details about Rishi Parashara are given below (quoting from the first link in my answer). He is also a Vedic Rishi to whom some Vedic mantras were revealed.
(i) He got the name Parāśara because even from the womb of his mother he consoled Vasiṣṭha when his son Śakti, father of Parāśara was eaten by the demoniac form of Kalmāṣapāda.
(ii) See under Guruparamparā the status of Parāśara in that traditional line of Gurus.
(iii) Among the Sūktas, Sūkta 65, Anuvāka 12, Maṇḍala 1 of Ṛgveda was sung by Parāśara.
(iv) Parāśara was one among the several sages who visited Bhīṣma lying on his bed of arrows. (Chapter 47, Śānti Parva).
(v) Once Parāśara visited king Janaka and talked with him on Ādhyātmika topics (spiritual matters). (Chapter 290, Śānti Parva).
(vi) Chapter 150 of Anuśāsana Parva mentions Parāśara as describing the power of Sāvitrīmantra to an audience.
Rishi Parashara is the Rishi of Suktas 65-73 of Rig Veda Mandala 1. Given below is a screenshot (from the book "Essentials of Rig Veda; R.L.Kashyap; Sakshi Publications) confirming the same.
Parashara Shaktya referring to Parashara as the son of Shakti.