Q&A for How to Capture Arceus in Pokémon Diamond or Pokémon Pearl

First, complete the pokedex. Then, continue to play the game for a few days. Then, check your town map. A certain pace will be by Vielstone City that wasn't there before. This place is the spring path. Bring a lot of repels with you, because there is a lot of tall grass. Continue through until you reach Turnback Cave. You need to find your way through the cave, and go through 3 rooms with 3 pillars. To make sure you are progressing, go up and click on the pillars. It will say 1, 2, or 3. After the third pillar, go straight. You know what to do.

I don't think so since I'm pretty sure that you can't breed legendaries (except Manaphy and Phoine). Unless you know a way to hack, then the answer is no.

A shiny has a very low chance of appearing, so it really just comes down to luck. However, there are methods to increase your chances.

Shinies are easier to catch with the shiny charm, which is obtained in the LilyCove hotel after filling the Pokedex, and trading can get you some good Pokemon.