How is two-strand cord braided? What shape cordage material works best for this technique? Do you need to start from relatively round cordage or can something strong but more flat (like a tough grass) be used?
You can easily* make two strand cord out of a variety of materials - I have done it with long grasses, but any relatively long fibrous material can work, including the fibres from inside woody stemmed plants, strips torn from a t-shirt, even plastic bags. Where you have flattish grasses, you can roll them between the palms to flatten them slightly and split the fibres apart a little - not completely, but enough to help them bind together.
Using relatively dry fibres, for example, from recently dead wood will allow you to bind the cord together more tightly than wet fibres, and in fact wet bound cord may separate as it dries, so do try to choose dry fibres where possible.
Avoid lining up the ends of fibres, as when you twist them together that would make a single point of weakness, so stagger the ends.
Then take two strands and twist them together - the key here is that if you are winding the fibres together clockwise as viewed from the end, you must twist each fibre in an anticlockwise direction.
Keeping the wrap tight is essential, especially when you bring in a new fibre - which you should overlap with the one which is ending.
(will try and pop in some diagrams when I get a chance, in case this isn't clear)
*easily - this can take hours and leave your hands aching, but anybody should be able to make two strand cord.*