Quite a few things to say about this. First of all, Fate/hollow Ataraxia is only a game (visual novel), no anime adaptation has been done yet. The first 2 openings are from the original PC game, and most of the images/CGs in the openings are taken from the game itself. The latter 2 openings are from the PS Vita remastered version; for those 2 ufotable did the animation (which is the studio that adapted Fate/Zero, Fate/Stay Night: Unlimited Blade Works and the Fate/Stay Night Heaven's Feel movies), while Aimer performed the vocals. As for the story, the game is a sort of sequel to the original Fate/Stay Night game, except it doesn't follow any of the 3 possible endings, and instead starts off in a "what if" alternate timeline. Lastly, in regards to that sphere in the sky... can't tell you unless you want spoilers.