Re: The bomb
I think you're reading too far into the "three months" comment. It was an off-the-cuff statement, designed to get one idea across - "these guys have been out of action and sitting in the dark since this began" and thus might not be up to the task of working as an army.
It wasn't an official number on a documented report or a scientific calculation. As a part of a conversation, it didn't need to be exact or completely accurate.
I think we can take the "five months" and "23 days" numbers to be much more accurate, however, as they're referencing very specific moments for which one CANNOT afford to be wrong about - the detonation of a nuclear bomb. "Five months" can still probably mean "give or take a week or two," though.
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