Unfortunately, we rely on information from the general web and from books for most of our research on these topics. Primary literature in peer-review journals offers some of the best information, and the topic of protein has been studied on Blattella germanica. These sources aren't as readily available to the general public without accounts through universities or some full-text prints available via Google Scholar. You'd be surprised how long it can take information from these sources to leak into the general public; I've met people who to this day believe a particular python complex is still considered subspecies of one another when a paper in 1998 raised each to full species status. 14 years, and people are still following the old nomenclature.
If you are interested in insect nutritional studies, I would review some literature by Mark D. Finke.
In addition to the paper on effects of protein on growth and reproduction of the German Roach (article I linked to you earlier), here is another paper of interest:
Jones, S. A., Raubenheimer, D. (2001). Nutritional regulation in nymphs of the German cockroach, Blattella germanica
Journal of Insect Physiology, Vol 47, Issue 10, September 2001, p 1169-1180.
1) Depends on the nitrogen concentration of the food item being offered. Grain products tend to be higher in protein, and are fine to add to the diet. Nitrogen is often a limiting nutrient in many insect diets and is often obtained through the digestion of amino acids. Plant material as a general rule is often high in carbon (i.e. cellulose and other complex carbohydrates) and lower in nitrogen. Some insects have evolved to thrive on high cellulose diets (termites) and termites and cockroaches are both within the same Order, Blattodea. Some cockroaches are known to contain protozoans to assist in cellulose digestion, so plant matter is undoubtedly a part of the natural diet. They are decomposers, they likely feed on detritus and other junk that falls to the forest floor in the neotropics (B. dubia).
2) Yes. It can influence them negatively in high concentrations. The type of protein is also an important consideration. I briefly talked this over with Kyle Kandilian at RoachCrossing and he too beleives that moisture is likely the bigger contributor to palatability of the food source. Other considerations are things like carotenoid concentration, which may very likely explain why oranges seems to yield better reproduction for some individuals.
3) Yes. But not in high concentrations like most people seem to think is essential in a good gutload.