To what extent have African Americans assimilated into US society?
This is a hugely complex question with a complex answer that cannot be adequately addressed in a space this size. The general answer is that different African Americans and different groups of African Americans have assimilated in different ways and to different degrees.
For example, poorer African Americans have assimilated in some ways but not in others. Their culture has come to resemble "mainstream" culture more than it once did. However, this may be as much from white America adopting such things as rap music and hip-hop styles as from any changes among black Americans. At the same time, they have not assimilated as much in terms of speech and in terms of their economic achievements.
More upper-class African Americans have assimilated to a greater degree. They have tended to move into more integrated communities and to attend integrated schools. Their children have become largely similar to white children of the same economic status.
Of course, all of these statements are gross generalizations that do not do justice to the diversity of experiences of individual African Americans.