Why is "can god kill god" a paradox? They either can or they can't (picking "they" because your particular god might not be a he). If they're all-powerful then the answer is yes, because they can do anything. I don't see how that's paradoxical.
If the answer is yes, then it negates "all-powerful" because it cannot withstand it's own power. Similarly, if "no", then it is not strong enough to destroy itself and, thereby, not all-poweful.
So, it's a paradox because "all-powerful" is typically used as "unkillable", but also carries a connotation of "can-destroy-anything". So, can something that is capable of destroying anything and cannot die kill itself?
Greek mythology had the dad-god "defeated" by being cut into literal pieces and scattered, but he wasn't really dead. And Zeus' siblings were eaten by his dad so they wouldn't usurp him, but they didn't die and he later puked them up.
But none of these were touted as all-powerful, biggest than bigger bigly, cannot be killed but can kill everything else.
A similar question on this line is can an all-powerful god make a rock too big for even said god to lift?
If the answer is yes, then it negates “all-powerful” because it cannot withstand it’s own power.
I disagree. If a god dies when it willingly chooses to die, that's not negating all-powerful. It has the ability to live and the ability to die; choosing one option or the other doesn't mean it never had the ability to do the option it didn't pick. Similarly, if a god chooses to never kill itself, that doesn't negate it being all-powerful, because it may have had the option to kill itself and just not done it.
A similar question on this line is can an all-powerful god make a rock too big for even said god to lift?
That's a much better paradox because that actually brings ability into it. Killing yourself only indicates the ability to kill yourself, not any lack of ability to do not-killing-yourself.