First off, I'm not claiming anything about Obito's defeat. Obito is inconsequential to this discussion as already pointed out. Whether he lived or died, he would have been Madara's puppet. Secondly, Zetsu does matter, because the entire claim about "luck" being involved is centered around Black Zetsu helping him and we are shown that Black Zetsu was always meant to do what he did (he declares that to Obito right before). Madara calling Black Zetsu to the battlefield hours before makes Zetsu's actions directly due to Madara's action, meaning there isn't anything lucky about Black Zetsu helping Madara. And thirdly, your argument doesn't even fit the situation. The phrase "beggars can't be choosers" only fits if said person has to do without something, which isn't the case here. Everything Madara intended still happened, the only change is simply the order of events.
Yes there is. His upper half not being able to move does not prevent the lower half from moving, as was clearly shown. Seriously, how could he have been defeated when we are literally shown he was capable of still fighting? That would be like someone trying to claim that when Naruto and Sasuke got knocked down by Obito, it was his win, and completely ignoring what was shown right after.