Your question seems to contain its own answer. If we read Celie's situation as being representative of the experience of African American women of the era, then all of the items you list become suggestive of a general experience.
Celie's separation from her children represents this trend during slavery where families were often broken up and sold off separately, their bonds not respected in law or in practice.
As a minority severely deprived of many avenues to upward mobility, comfort, and political participation, African Americans and African American women in the South through the Jim Crow period were often denied access to education.
Reading Celie's character and her story as a symbolic representation of the plight of her demographic, as it were, offers some power. Celie's success in the latter sections of the novel - her achievement of confidence, of peace, and reunion - become the successes of a whole class of people.
With this being said, discussions of symbolism in the novel will not usually be so broad. The novel is not an allegory. Discussions of symbolism will often focus more on discrete ideas, objects, or characters that can be seen to play a part in creating meaning within the context of the work.
The discussion situating the entire story as a symbol suggests allegory and attempts to interpret ways in which the novel creates meaning within a context larger than itself.
This is not wrong to do, but following this line of discourse has the potential to obviate the craft of the work, looking at the outlines of the novel instead of at its inner workings. There is a danger of over-simplifying.