1) Book of Mormon prophecy regarding the 8 witnesses
Like the three witnesses, the Book of Mormon prophecies that there will be others which will testify of this work, And there is none other which shall view it, save it be a few according to the will of God, to bear testimony of his word unto the children of men; for the Lord God hath said that the words of the faithful should speak as if it were from the dead. Wherefore, the Lord God will proceed to bring forth the words of the book; and in the mouth of as many witnesses as seemeth him good will he establish his word; and wo be unto him that rejecteth the word of God. (2 Ne 27:13-4)
2) How many people actually saw the plates?
Whenever Joseph carried the plates around the house, he kept them covered by a cloth of some type. Therefore, all of his family members saw the plates while bundled up but only Joseph Sr., Hyrum, and Samuel saw the plates uncovered. This they did as part of the group of eight witnesses. The total number of those who saw the actual plates is twelve, excluding Joseph Smith. These include the three witnesses, the eight witnesses, and Mary Whitmer:
"[According to David Whitmer,] soon after our [Joseph, Oliver, and David] arrival home [in Fayette], I saw something which led me to the belief that the plates were placed or concealed in my father's barn. I frankly asked Joseph if my supposition was right, and he told me it was. Sometime after this, my mother was going to milk the cows, when she was met out near the yard by the same old man (judging by her description of him) who said to her: 'You have been very faithful and diligent in your labors, but you are tired because of the increase of your toil; it is proper therefore that you should receive a witness that your faith may be strengthened.' Thereupon he showed her the plates. My father and mother had a large family of their own, the addition to it therefore of Joseph, his wife Emma and Oliver very greatly increased the toil and anxiety of my mother. And although she had never complained she had sometimes felt that her labor was too much, or at least she was perhaps beginning to feel so. This circumstance, however, completely removed all such feelings and nerved her up for her increased responsibilities." ("Report of Elders Orson Pratt and Joseph F. Smith," Millennial Star 40 (9 Dec 1878):772-73 as taken from Testimony of the Book of Mormon Witnesses by Preston Nibley)
"[John C. Whitmer said that] my grandmother told me that the strange visitor met her as she was going to milk the cows. At first she was afraid of him, but he spoke so kindly to her, explaining to her the nature of the work of translation to go on in her house, that she felt a thrill of inexpressible joy, which removed all fear from her. Comforting words were spoken, promising her strength and pleasure in her increased labors, and salvation at the end. Moroni took from his knapsack the plates and exhibited them as already explained by David. The personage then suddenly vanished with the plates, and where he went, she could not tell. From that time my grandmother was enabled to perform her household duties with comparative ease, feeling no inclination to murmur because her lot was a hard one." (Edward Stevenson, "The Thirteenth Witness to the Plates of the Book of Mormon," MS 55 (1893):215 as taken from Testimony of the Book of Mormon Witnesses by Preston Nibley)
3) Background on the 8 witnesses
The work of the translation was proceeding nicely in Harmony, Pennsylvania for quite a while. But Joseph's father-in-law was not very patient with Joseph's ecclesiastical endeavors. It soon became evident that a new residence was needed. After communicating with David Whitmer, Oliver and Joseph decided to move to Fayette, NY to the home of Peter Whitmer, Sr. At this residence, Oliver and Joseph's family had free board. The Whitmer brothers, Christian, Jacob, John, David, and Peter Jr. were very interested in the work. David was privileged to become one of the three witnesses. The other four along with their brother-in-law Hiram Page were shown the plates as their testimony describes. Hiram was later the cause of some confusion in the church because he claimed to be receiving revelations through a seer stone (see DC 28).
In June of 1829, while the translation was underway, John Whitmer and Peter Jr. had Joseph inquire of the Lord regarding their calling and status. The result is DC 15 and 16 (see headings). Six of the eight witnesses of the Book of Mormon received special messages directly from the Lord through Joseph Smith:
John Whitmer DC 15, DC 26, DC 30
Peter Whitmer, Jr. DC 16, DC 30
Joseph Smith, Sr. DC 4
Hyrum Smith DC 11
Samuel H. Smith DC 23
Hiram Page DC 28
Not unlike the 3 witnesses, not all of the 8 witnesses remained true to the faith. In fact, Jacob Whitmer, John Whitmer, and Hiram Page fell away. The other 5 died in full fellowship.
4) What is the difference between what the 3 witnesses saw and what the 8 witnesses saw?
Oliver Cowdery, David Whitmer, and Martin Harris were shown the plates, the sword of Laban, the breastplate, the Liahona, and the Urim and Thummim by Moroni. They did not handle the plates but saw an angel who spoke with them and commanded them to testify of what they saw. They also heard the voice of the Lord declaring the truth of these things.
The eight witnesses saw no angel. They heard no voices. They were shown the plates by Joseph Smith. There testimony was to be that they had seen and handled the plates-to prove to the world that Joseph Smith actually had possession of an ancient record.