Because Decade can do whatever he wants and show up wherever he wants, and people will insert him in whatever series they want because they can. Get used to it.
actually i think when he did his rider kick he utilized this although it was a pretty shitty eagle vision.
lion is for the roaring probably, kuwagata... i have no clue.. multiplying? Rhino, probably for a rider headbutt. i can totally imagine sagorzo charging on all fours and ramming his opponent.