It hasn't totally been explained as far as I know, but it's generally assumed that the rings limit and control his chaos energy use and possibly help store energy. When he takes them off, there's a rush of power allowing for a temporary boost of strength.
inhibitor rings
he doesn't shadow does; however have rings on his shoes and wrists
she sang shadow
Removal of Shadow's inhibitor rings results in him getting a surge of power, but after a while he will get exhausted so he doesn't use it very often.
Not as far as we've seen. The Darkspine transformation is triggered by the World Rings, which have thus far only been in Sonic and the Secret Rings, and no incarnation of Shadow, normal or Arabian, was seen in Secret Rings.
First, I should tell you during Solaris, all three hedgehogs have 50 rings to start with. They are constantly losing them, especially when they are hit. In order to keep from killing one of them, you need to switch between them to help the other gain health. Switch between them whenever one of the other hedgehog regards their rings. The order of switching hedgehogs is Sonic-> Shadow-> Silver-> Sonic. The hedgehogs gain rings when not being used up to 50, but only at the same pace that they lose them. Do not switch through them as fast as you can. At first, you can only attack with Super Silver, by catching the boulders Solaris throws at you, then throwing them back at it. Next, (you will know when you have done enough damage) Only Super Shadow will be able to damage him. Charge your Chaos Spear, then throw them at him. Something similar that happened to Silver will happen to Shadow on the other arm. Now you will use Super Sonic. Fly into Solaris at top speeds (I think you have to charge them up first). Then is Solaris phase two. (Here is the best Sonic music EVER for a final boss) Now you can attack using any of the three super hedgehogs to defeat Solaris. Hope this helped!
Saturn is the planet you are talking about for its rings are sometimes obscured from view by Saturn's shadow.
He removes his rings to have an increase in power, but at the cost of lowering his stamina.
Get 30 fire souls (red rings). He can only be played in party mode.
Shadow doesn't have a health bar, but he loses 10 rings after taking damage
Nothing it just rings
Shadow wasn't in the storyline. he was only a party character selection. He never wished for anything.