In addition to being China's first administrators, in the sense that they developed a coherent bureaucracy for their empire, the first literate culture in East Asia were the Shang, and they were well known for crafting ornate bronze ritual vessels.
A and B result in misplaced modification - the first literate culture wasn't "china's first administrators"
(A) the first literate culture in East Asia were the Shang, and they were well known for crafting
(B) the first literate culture in East Asia were the Shang, well known as the crafters of
In C "is well known for its crafting ornate bronze ritual vessels" just doesn't make sense even if the subject and verb did agree, which they don't. C is analogous to saying "the English, as the first literate culture in Australia, is well known for its crafting ornate bronze ritual vessels". Obviously there are SV Agreement issues here, but the less blatant issue is that a culture is well known for something. The correct answer changes "crafting" to "known as the crafters of", which correctly refers to the individuals within the group.
(C) the Shang, as the first literate culture in East Asia, is well known for its crafting
D is correct because the subject, the Shang, agrees with the plural verbs "were"and "are, which are logically placed parallel
(D) the Shang were the first literate culture in East Asia and are well known as the crafters of
E is incorrect because a plural verb and singular pronoun are used to refer to "The Shang"(plural). The "its" should be "their"
(E) the Shang were the first literate culture in East Asia and well known for its crafted