It is said that Lord Krishna was a human being with qualities of God, thus Lord Krishna has a special place in sanatana dharma. I would like to understand, if Veday Vyasa has written Mahabharata, whether he has seen Lord Krishna and therefore he was able to write so much about Lord Krishna in Mahabharata and later in Bhagavatham. I also have read that Veda Vyasa is also known as 'Krishna Dwaipayan'. Does it mean that Veda Vyasa himself is krishna?
Yes. Vyasa saw and met Sri Krishna many times but this wasn't how Vyasa wrote Mahabharata. One such meeting happened during Brahmastra episode of Arjuna and Aswathama. Indeed, Kauravas are biological descendants of Vyasa.
Vyasa with his Trikaladarshi powers analyzed Vedas and taught Puranas to his disciples. Here is what Chapter one of Adi Parva of Mahabharata says:
The son of Satyavati having, by penance and meditation, analysed the eternal Veda, afterwards composed this holy history, when that learned Brahmarshi of strict vows, the noble Dwaipayana Vyasa, offspring of Parasara, had finished this greatest of narrations, he began to consider how he might teach it to his disciples.
And it was thus that Vyasa was born of Satyavati through Parasara. And because he was born in an island, he was called Dwaipayana (Dwaipa or islandborn). And the learned Dwaipayana, beholding that virtue is destined to become lame by one leg each yuga (she having four legs in all) and that the period of life and the strength of men followed the yugas, and moved by the desire of obtaining the favour of Brahman and the Brahmanas, arranged the Vedas. And for this he came to be called Vyasa (the arranger or compiler).
Since Krishna Dwaipayana Vyasa is Vishnu and Krishna is also Vishnu, you can consider Vyasa as Krishna though they differ in some qualities or attributes.
Yes he did. There is an interesting story of how Vyasa saw Krishna.
First, Vaishampayana explains that Vyasa was son of Narayana.
Vaisampayana said, "I bow unto that great Rishi who is the dispeller of darkness, and whom Satyavati bore to Parasara in the midst of an island, who is possessed of great knowledge and who is endued with great liberality of soul. The learned say that he is the origin of the Grandsire Brahma; that he is the sixth form of Narayana; that he is the foremost of Rishis; that he is endued with the puissance of Yoga; that as the only son of his parents he is an incarnate portion of Narayana; and that, born under extraordinary circumstances on an Island, he is the inexhaustible receptacle of the Vedas. In the Krita age, Narayana of great puissance and mighty energy, created him as his son. Verily, the high-souled Vyasa is unborn and ancient and is the inexhaustible receptacle of the Vedas!"
Janamejaya asked how Vyasa was son of Narayana.
Janamejaya said, "O best of regenerate persons, it was thou that saidst before this that the Rishi Vasishtha had a son of the name of Saktri and that Saktri had a son of the name of Parasara, and that Parasara begot a son named the Island-born Krishna endued with great ascetic merit. Thou tellest me again that Vyasa is the son of Narayana. I ask, was it in some former birth that Vyasa of immeasurable energy had sprung from Narayana? O thou of great intelligence, do tell me of that birth of Vyasa which was due to Narayana!"
Vaisampayana told how he had the same question to Vyasa.
Vaisampayana said, "Desirous of understanding the meaning of the Srutis, my preceptor, that ocean of penances, who is exceedingly devoted to the observance of all scriptural duties and the acquisition of knowledge, dwelt for some time in a particular region of the Himavat mountains. Endued with great intelligence, he became fatigued with his penances in consequence of the great strain on his energies occasioned by the composition of the Mahabharata. At that time, Sumanta and Jaimini and Paila of firm vows and myself numbering the fourth, and Suka his own son, attended on him. All of us, O king, in view of the fatigue our preceptor felt, waited dutifully upon him, engaged in doing all that was necessary for dispelling that fatigue of his. Surrounded by these disciples of his, Vyasa shone in beauty on the breast of the Himavat mountains like the Lord of all the ghostly beings, viz., Mahadeva, in the midst of those ghostly attendants of his. Having recapitulated the Vedas with all their branches as also the meanings of all the Verses in the Mahabharata, one day, with rapt attention, all of us approached our preceptor who, having controlled his senses, was at time rapt up in thought. Availing ourselves of an interval in the conversation, we asked that foremost of regenerate persons to expound to us the meanings of the Vedas and the Verses in the Mahabharata and narrate to us the incidents as well of his own birth from Narayana. Conversant as he was with all topics of enquiry, he at first discoursed to us on the interpretations of the Srutis and the Mahabharata, and then set himself to narrate to us the following incidents relating to his birth from Narayana.
He recounts how Vyasa told about his former birth
After this, the original Creator of the universe once more uttered the syllable, Bho, causing the atmosphere to resound with it. From this syllable of speech (Saraswati) arose a Rishi of the name Saraswat. The son, thus born of the Speech of Narayana, came to be, also called by the name of Apantara-tamas. Endued with great puissance, he was fully conversant with the past, the present, and the future. Firm in the observance of vows, he was truthful in speech.
Later, he even said how Apantaramas in the kalpa named after the self-born arranged the vedas which gratified Vishnu.
Unto that Rishi who, after birth, had bowed his head unto Narayana, the latter, who was the original Creator of all the deities and possessed of a nature that was immutable, said those words: Thou shouldst devote thy attention to the distribution of the Vedas, O foremost of all persons endued with intelligence. 2 Do thou, therefore, O ascetic, accomplish what I command thee.--In obedience to this command of the Supreme Lord from whose Speech the Rishi Apantaratamas sprang into existence, the latter, in the Kalpa named after the Self-born Manu, distributed and arranged the Vedas. For that act of the Rishi, the illustrious Hari became gratified with him, as also for his well-performed penances, his vow and observances, and his restraint of the senses or passions.
Vishnu said how Apantaramas will take birth as Vyasa in the lineage of Vashishta.
Addressing him,--Narayana said,--At each Manwantara, O son, thou wilt act in this way with respect to the Vedas. Thou shalt, in consequence of this act of thine, be immutable, O regenerate one, and incapable of being transcended by any one. When the Kali age will set in, certain princes of Bharata's line, to be called by the name of Kauravas, will take their birth from thee. They will be celebrated over the Earth as high-souled princes ruling over powerful kingdoms. Born of thee, dissensions will break out among them ending in their destruction at one another's hands excepting yourself. O foremost of regenerate persons, in that age also, endued with austere penances, thou wilt distribute the Vedas into diverse classes. Indeed, in that dark age, thy complexion will become dark. Thou shalt cause diverse kinds of duties to flow and diverse kinds of knowledge also. Although endued with austere penances, yet thou shalt never be able to free thyself from desire and attachment to the world. Thy son, however, will be freed from every attachment like unto the Supreme Soul, through the grace of Madhava. It will not be otherwise. He whom learned Brahmanas call the mind-born son of the Grandsire, viz., Vasishtha endued with great intelligence and like unto an ocean of penances, and whose splendour transcends that of the Sun himself, will be the progenitor of a race in which a great Rishi of the name of Parasara, possessed of mighty energy and prowess, will take his birth. That foremost of persons, that ocean of Vedas, that abode of penances, will become thy sire (when thou wilt take birth in the Kali age). Thou shalt take thy birth as the son of a maiden residing in the house of her sire, through an act of congress with the great Rishi Parasara.
Vishnu also said that he will see him as Krishna and in his next birth as Krishna-Dwaipayana Vyasa, he will have no doubts of past, present, and future.
Doubts thou wilt have none with respect to the imports of things past, present, and future. Endued with penances and instructed by me, thou wilt behold the incidents of thousands and thousands of ages long past away. Thou wilt see through thousands and thousands of ages also in the future. Thou shalt, in that birth, behold me, O ascetic,--me that am without birth and death,--incarnated on Earth (as Krishna of Yadu's race), armed with the discus. All this will happen to thee, O ascetic, through the merit that will be thine in consequence of thy ceaseless devotion to me. These words of mine will never be otherwise. Thou shalt be one of the foremost of creatures. Great shall be thy fame. Surya's son Sani (Saturn) will, in a future Kalpa, take birth as the great Manu of that period. During that Manwantara, O son, thou shalt, in respect of merits, be superior to even the Manus of the several periods. Without doubt, thou shalt be so through my grace.
This is how Vyasa was able to see Krishna.