To easily defeat Blue-Eyes Shining Dragon, use cards that don't target a specific monster on the field (Dark Hole, Mirror Force, Raigeki, etc.), since that monster's effect states that it can't be defeated by card effects that target this specific card.
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Yes, blue-eyes shining dragon can destroy a rainbow dragon.
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Yes it does. Lightning Vortex does not target. Blue-Eyes Shining Dragon's protective effect works only against cards that target, like Exiled Force.
No, if you look at Blue-Eyes Shining Dragon's text, it says it cannot be special summoned, except by tributing a Blue-Eyes Ultimate Dragon from your side of the field.There is simply no way around this. It is the only way it can be summoned.
In terms of attack, yes, "Obelisk the Tormentor" and "The Winged Dragon of Ra" (if it has enough attack) can beat "Stardust Dragon".However, if you are referring to the destruction effects of "Obelisk" and "Ra", then "Stardust Dragon" does "beat" them since it can negate their abilities and destroy them.