1) I think they do. Luffy's DF changed the constitution of his body, as logias change the constitution of the people who eat them. Luffy's stretching/twisting is a usage of his ability. He is rubber, he stretches. Akainu is magma he shoots magma fists.
I don't think that is a good analogy.
Let me explain, first, why I don't think Luffy is a good counterexample to the argument that Devil Fruit abilities drain stamina. The Gomu Gomu no Mi makes Luffy's body like rubber. It is a property that is "acted upon", meaning that Luffy uses his physical strength and muscles to tense and stretch his body in order for attacks. In that sense, "stretching" is the same as a physical motion. I don't count it as an example of a Devil Fruit ability that drains stamina, because in this case, the physical movement is what's draining stamina. But you can't count it as evidence that Devil Fruits don't drain stamina, because the Gomu Gomu no Mi is not representative of all Devil Fruits.
So, Akainu. This isn't a good analogy because there is no reason to think that all his abilities are passive, like Luffy's. For example, I don't think his intangibility is something that drains stamina. It's a property of his magma body that is shown when his body is "acted upon". But you can't argue that this doesn't use stamina (or "magma energy"). That ability is not a passive property of Akainu's body. It's not a simple punch with a hand that is made of magma (which you can argue drains physical stamina). It either involves the production of more of his element or an intensification of the element that is already there, depending on how you think Logia abilities work. It's not analogous to Luffy's Devil Fruit, because Luffy does not have an ability like that.
2) Sure it doesn't but I don't see the change requiring stamina at least not in the sense that Law/Caesar seem to need stamina for their abilities.
Having said that, if the change required stamina why wouldn't maintaining the state require stamina? I personally don't believe either do.
I don't know whether, in fact, the change requires stamina. My point is that as long as you accept that being in a particular form may not require extra stamina, what you said ("We've never seen Chopper tired from staying in his half man half deer state.") doesn't help your case. There's no reason to think he needs to "maintain" his hybrid form, as if somehow, without stamina, he'd change into another form. (Unconscious Chopper remains in his hybrid form, by the way. 1 2 (As did Lucci and Jyabura.) Not sure it counts for something, but it might.) (Btw, I'm not counting stamina expended just from living, like daily calorie burn or something. Taking that into account, it's possible to argue that his hybrid form takes less energy than his other two forms.)
Nobody has mentioned a stamina drain or shown a stamina drain.
Part of your argument relies on "absence of evidence" being "evidence of absence". There are circumstances in which I would agree with that kind of reasoning, but this case isn't one of them. So far, most of your examples have been "x was never tired", which, of course, doesn't logically entail "x's abilities don't use stamina, nor can it be counted as strong evidence for "x's abilities probably don't use stamina", because the (not so unlikely) possibility that these characters have massive stamina exists. Given that, it's not surprising that we don't see characters complaining about stamina.
However, it's not actually true that we don't see characters complaining about stamina. In your view, Caesar, Law and now Marco are exceptions. But they're also evidence against your view. I don't think it's likely that your view is the correct one, because I don't see how you're justified in saying these are exceptions (and further, how your view explains the existence of these exceptions. Caesar's is the most problematic, in this respect)
Also, this might be another example of "stamina" failing, though of course, it can be attributed to consciousness or damage as well:
Edited by Tale, 21 October 2014 - 08:47 AM.