Yes. Winged Dragon of Ra only stops effects being used directly against his summon, ie, 'When' he is summoned. It is not a continuous effect that permanently shuts down spells, traps and monster effects.
No part of Winged Dragon of Ra's effect stops you from Special Summoning while you have him out on the field.
When he is summond on the field your oponent will lose
It's first special ability is that it can't be special summoned, though it's more a restriction. Second is that his normal summon can't be negated. Also, when he's normal summoned, spells, traps and monster effects can't be activated. And, you can lower your Life Points to 100, The Winged Dragon of Ra will get Attack and Defence points equal to the Life points paid. And last, you can pay 1000 Life Points to select and destroy one monster on the field.
You will be able to use its effect while you control "D.D. Survivor" and/or "D.D. Scout Plane". The card's effects will banish then and it will return to the field.
According to the effects of Slifer the Sky Dragon given in Yu-Gi-Oh! 5D's World Championship 2010: Reverse of Arcadia, Bottomless Trap Hole may not be activated when it is Tribute Summoned onto the field. It clearly states that "...when this card is Normal Summoned, the effects of Spell, Trap, and Effect Monster Cards cannot be activated..."Slifer the Sky Dragon can be destroyed afterwards by cards that do not target it, such as Mirror Force, or Widespread Ruin.
Yes, "Skill Drain" can negate the effects of "The Winged Dragon of Ra" while the monster is on the field. "Skill Drain" does not target any monsters, it simply affects them.If "The Winged Dragon of Ra" gained attack via tributing monsters during its Tribute Summon or paying Life Points, its ATK would be 0. However, if the controller of "Ra" were to use its effect and tribute "Ra" to destroy a card on the field, it would work. This is because as a part of the cost before applying the effect, the player must pay Life Points and sacrifice "Ra". The actual effect then takes place from the Graveyard and "Skill Drain" only affects monsters on the field.
The turn player has "priority" of effects to be activated first, but in the event that two Trigger effects are activated simultaneously, as in this case, they are put on the Chain in the following order: Turn player's mandatory effects, opponent's mandatory effects, turn player's optional effects, opponent's optional effects. So, technically, they activate simultaneously, but when they are put upon the Chain, they resolve in reverse order of when they are put on. In short, Number 57's effect resolves first.
Stardust Dragon can only be used against effects that will destroy a card on the field.
if you sacrifice ra and slifer while obelisk is on the field obelisk wood have infinite attack and nothing can stop him
Unless specifically stated otherwise (Royal Oppression, etc), you can only activate the effects of a card you have control of. If 'your' Winged Rhynos is on the opponent's side of the field, then in game terms, it is 'his' monster. He's the only one that can activate the effect.
Light and Darkness Dragon only affects the initial activation of a spell or trap, ie, the time it is placed on the field face-up, or flipped face up as it is activated. Once resolved to the field, these cards are unaffected by Light and Darkness Dragon, cards like Pitch Black Power Stone and Royal Oppression use the chain when they activate their subsequent effects, but Light and Darkness Dragon will not chain to these.
His ATK-boosting trigger lasts until he leaves the field or is flipped face-down. If that happens, the bonus is lost.