@Flushed:
Ok so lets make a fake scenario. Your battling competitively against a lvl 100 Shiny Pikachu with your lvl 100 regular Pikachu that you've bred specifically for competition. Is it safe to assume that the regular Pikachu will probably have better stats than the Shiny Pikachu, and any other Shiny Pikachu's he ever encounters?
Ok so lets make a fake scenario. Your battling competitively against a lvl 100 Shiny Pikachu with your lvl 100 regular Pikachu that you've bred specifically for competition. Is it safe to assume that the regular Pikachu will probably have better stats than the Shiny Pikachu, and any other Shiny Pikachu's he ever encounters?
Shinyness is not connected to IVs, thus the answer to 1) is no (assuming random encounter). When you breed for a shiny (or any Pokemon for that matter), if the parents have good IVs and a Destiny Knot, etc. etc. then they may possibly have better IVs, so the answer to 2/3 is possibly.