You cannot solo the mini game. there is a 2 player minimum like castle wars (or any free player mini games.) you might of heard someone say that but in fact they just might of not encountered the other player (which is very unlikley, but happened to me once.)
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You can buy most stuff at the Grand Exchange. You can also buy talismans from the Great Orb Project (you get points from that game, that you can redeem for items, including talismans.)
You can. At the end of each altar (known as a "round") in the Great Orb Project mini-game, each player is automatically given Rune Essence (Pure Essence if on a Member world) based on the score they received in that round. You will always get at least one Rune Essence as you receive it automatically, even if your team did not score any. Players may use these Rune Essence to craft runes at the current altar of the round to gain experience and obtain runes before entering the portal to the next altar. Other than this, playing the activity itself will not grant a player any experience in Runecrafting.
Let Palkia hold the lustrous orb, and let Dialga hold the adament orb. It boosts their special moves' damage.
the red orb gives you the chance to catch groudon and the blue orb gives you the chance to catch kyorge.
It is called the Griseous Orb.