Once you use a Generate Modifier (decimate counts as well) you don't have much control over the mesh anymore. Since modifiers are by nature dynamic, you can't change individual faces, since they might not exist in another frame.
Usually you would use vertex paint in a situation like this, but that's also not easy.
One method to cheat I can think of right now ...
My previous answer won't give a correct method.
Actually the Snap option would work correctly if it was compatible with GG (slide vertex along an edge) but it's not the case yet.
What you should do to get edges perpendicular to the X, Y and Z axis is use the knife tool: K to activate, C to cut orthogonally to an axis, Z to cut through.
Once you've created ...
Try the F2 addon. It's already built into Blender, but isn't enabled by default. When it's active, pressing the 'f' key with a vertex selected extrudes an entire face from it instantly and allows you to continue adjusting its position afterwards. Really speeds up modeling and retopology efforts.
TheBeautifulOrc technically has the right answer. However, based on my personal experience, I would say that the shrinkwrap modifier, while very useful in some cases, could be problematic in your case. It may actually be easier to take the Genesis 8 model from Daz Studio, import it into Blender, take your custom model also, and import that into the same ...
If I understand your question correctly,you are looking for the Shrinkwrap-Modifier. Add the modifier to the model you want to change and choose your "desired face" as the target. For further reading consult the manual.
However there is no way to get more detail than your polycount allows. That means the Shrinkwrap-Modifier might produce artifacts if the ...
You must have overlapping vertices. Before pulling the edges, select all (A) and altM > Merge By Distance to make sure you've deleted those vertices (check the Operator box on the bottom left of the 3D view to play with the threshold)
In the top bar there will be two orientation parameters when you click the MOVE tool. The first should be "default", make the second one "Normal" from the drop down menu. Move your face now in the desired direction.
A script to do this
Shows origin and local orientation of one split off face
Adds an icosphere, edge splits, separates and returns to object mode
Selected objects are the result of separate modifier.
For each face object get its lone face and calculate the global center and normal. See how far the normal is rotated from default quaternion.
Use this to ...
Ideally, that face should reassemble a grid made out of quads (polygons of 4 vertices) so that when you sculpt it, the resolution is more or less equal along the entire mesh
The fastest way to do so would be to delete that big face on the middle, selecting the edge loop (Alt+Click) corresponding to the face you just deleted and in the face properties menu (...
By default the extrusion will follow the face normal (it's orientation). If it's not vertical the extrusion won't be either. To extrude and constrain on the Z axis just press E then Z.
Also, for this kind of faces that stick to the mirror axis, if you enable the Mirror Clipping option it will prevent the creation of a face on the axis itself.