Is there a cute form for Ahmed? How I can address a little boy, for example, or how a mum calls her son. I've heard something like Ahmoody but I'm not sure that's the right one
You may be right. I will say that I've never heard حمادة as a nickname at all. Perhaps there are regional differences with regard to how common or popular different nicknames are.
Of course, since these names share the same roots, I also think this same way but I just displayed the combinations I heard the most frequently though anyone is free to choose any of them.