I have a question.

If I put the Red Lantern Ring, which gives the character to which it is attached penetrating poison, on the ASM Man-Thing with its "Whatever Knows Fear..." power:

WHATEVER KNOWS FEAR...: Man-Thing can use Poison. When he does, instead of dealing normal damage, roll a d6 that can't be rerolled for each adjacent opposing character. On a result of 1-3 deal that character 1 damage. On a result of 4-5, deal that character 2 damage. On a result of 6, deal that character 3 damage.

will the poison generated by Man-Thing's special power become penetrating because he has the Red Lantern Ring attached?

Man-Thing will not be able to use the Poison granted by the ring at all, because he can use Poison naturally.

Oh, so the penetrating poison granted by the Ring can only be used by characters that cannot normally use Poison as part of their standard powers?

Correct. You can't gain the use of a power from an outside source (eg. a Relic or Resource) if you can already use that power.

I'm pretty sure you get to choose which form of a power you use if you have two sources of it.

No, you don't.

As already stated, if you can already use an effect, you can't get a second use of it. So if your character already has Poison, it can't get Poison from a different source.

On top of that, I believe that if a character is using the special Poison from the ring, and then gets normal Poison on their dial, they default to using the dial Poison.

I believe you are thinking of when a character is granted a power by more than one exter game effect at the same time. The you get to choose which one you wan't to use. However you will be stuck with that version until it is lost. Or that power is granted by the dial.