adding faces to faces - may not be correct term.

If this is not fake:

how does one add the missing squares to something like this? that big empty triangle:

squares within squares / faces/within faces?.

Preferably with F2 addon and snap to surface enabled. You can also just extrude those square and use shrinkwrap modifier while you do it, pretty simple If you ask me. I must admit that I don’t really see the problem here, this is pretty mandatory in 3d modeling.

Watch a few video tutorials on modelling in Blender to learn the basics. I recommend Darrin Lile’s youtube series on moselling. He’ very easy to follow.