If you eat certain eels uncooked, you can die from internal bleeding. The blood of the eel has a toxin which prevents coagulation. Why doesn't the eel bleed to death?

Eels are cold-blooded so it does not affect them as it would a warm-blooded person.

I'm not sure that warm blooded and cold blooded come into it.
It might do if it were to eat another one.
The toxin/poison/venom has to be in the right place.
Why does a snake not die of the poison it manufactures in its own body? Why does an electric eel not kill itself?

There are many snake venoms that will kill you if they enter your blood stream but you could drink a pint of them and, providing you do not have stomach ulcers, it would be perfectly safe.

Why does your stomach not digest itself ?

the stomach doesn't digest itself because it has a protective layer of mucus.
some snakes can die if they bite themselves but for example the cobra has sugar molecules in the nerve's recievers and senders and the venom protein can't shut them off because the sugar protein and the venom protein do not fit so they don't bind and the venom can't block the impulses from and so the snake doesn't paralize itself.
I don't know about electric eels though.
the toxin in eels is in the BLOOD, and the toxin works on the BLOOD to stop it from coagulating. get my point? (I don't mean to offend anyone but I am a bad explainer..)