So I have questions regarding two cards I haven't been able to find an answer to.

When the character One with the Force is attached to dies it becomes a ready support, I'm clear on that, but what happens to the die?

If the dice is already in the pool does it stay there or go back to the card? And if it stays does that mean it can be used again since One with the Force starts ready?

The second cards is Natural Talent.

Is it possible to use it on the special side, to resolve the targeted ability twice? And if not, can it even target a special side?

The die remains in play (OWTF says it happens BEFORE the character is defeated so it's die isn't removed) and yes you could then resolve that die, return it to the card and then activate it again.

Yes, you could resolve a special but the increase in value part would be unused. Specials have no value.