I'm not a US legal scholar but I wouldn't be surprised to know the US Supreme Court might have ruled that such rights do not apply to non-US citizens.
No declaration of war was made on Iraq.
Yes, it was; no special language is needed in a declaration of war; the "Authorization for the Use of Military Force" was plainly and unmistakeably a conditional declaration of war, the conditions for which were fulfilled.
The applicability of the Geneva Conventions is affected by the fact of war, but independent of whether there is a declaration. And even if it wasn't, violations of the Conventions would not reach back in time and change whether a declaration had occurred.
an officer can order hundreds of soldiers to charge into certain death without repercussions - as long as the military goal he's trying to achieve is justifiable.
There was never a formal declaration of war on Iraq. Just saying.