Unless stated otherwise on the card, a special summon is in face-up attack or face-up defence mode. Cyber Dragon doesn't specify a specific position, so can be placed in either of the two default positions above.
Call of the Haunted is one card that is specific, the monster is summons can only go in face-up attack mode. The Shallow Grave is another specific one, this one Special Sets, rather than put the monsters in the default face-up positions.
Cyber Dragon doesn't have any activated effects. Cyber Dragon's special summon can only be performed on your own turn, in your main phases.
As long as the 'Cyber Twin Dragon' was properly summoned initially, by Fusion Summon, and was then destroyed, then yes, you can resummon it from the graveyard with 'Call of the Haunted'. If the 'Cyber Twin Dragon' got to the graveyard by the following methods - sent from Extra Deck by 'Gale Dogra', special summoned but not Fusion Summoned by 'Cyber Stein', or had its Fusion Summon negated, then it cannot be special summoned from the graveyard.
no, dragon master knight can only be fusion summoned.
No, Divine Wrath can only be used against effects that activate. Most of the time, when a monster has a way to special summon itself, this is an inherent special summon, just like a normal summon, it does not use the chain. Because it doesn't use the chain, you can't chain an effect negation card to it, though you can use summon negation cards like Solemn Judgment. If the special summon is an activated effect (like Dandylion's effect to special summon tokens, or Gorz's effect to summon himself) then these can be stopped using Divine Wrath. But Cyber Dragon's special summon cannot.
Unless specifically stated otherwise, a monster special summon method is for when it is in the hand only. So Treeborn Frog special summons itself from the graveyard because the effect says so. But Cyber Dragon special summons from hand - even though it does not say so, the hand is the default zone, it cannot special summon itself from the gfraveyard. Likewise, Hardened Armed Dragon must be in your hand to use its special summon effect.
well judging by you question, I'm assuming that your opponent has a monster on the field. if that's the case then yes, since cyber dragon's effect lets you special summon it-which doesn't count as a normal summon-which means you can still normal summon on the same turn.
You can only tribute one "Cyber Dragon" on the field with "Attack Reflector Unit" in order to Special Summon "Cyber Barrier Dragon".
Cyberdark Dragon cannot be summoned except by Fusion Summon. Cyber Stein does not 'fusion summon' the fusion monsters is summons, it is only a special summon. It therefore cannot summon monsters like Dark Paladin, or Cyberdark Dragon.
No, the text for Cyberdark Dragon says: "This monster cannot be Special Summoned except by Fusion Summon..."
Cyber Dragon doesn't have any activated effects. Cyber Dragon's special summon can only be performed on your own turn, in your main phases.
As long as the 'Cyber Twin Dragon' was properly summoned initially, by Fusion Summon, and was then destroyed, then yes, you can resummon it from the graveyard with 'Call of the Haunted'. If the 'Cyber Twin Dragon' got to the graveyard by the following methods - sent from Extra Deck by 'Gale Dogra', special summoned but not Fusion Summoned by 'Cyber Stein', or had its Fusion Summon negated, then it cannot be special summoned from the graveyard.
Yes. The whole idea behind Proto-Cyber Dragon's name changing effect is to let it be used for Cyber Dragon support and fusion.
Yes. Like Cyber Dragon, Gorz 'can' special summon himself with his effect, but he is not a 'special summon only' monster, he can be tribute summoned with two tributes, if you want.
Cyber Laser Dragon cannot be special summoned 'except' by following the text on its own card. Even if you properly special summon it by this method, you cannot resummon it from the graveyard by cards like Monster Reborn, or De-Fusion.
If you are talking about its effect to Special Summon a Fusion Monster with his effect, you can't. You have to have both The Light - Hex Sealed Fusion along with another Fusion Material, for example Cyber Dragon to Summon Cyber Twin Dragon, and Tribute both of them, and Special Summon Cyber Twin Dragon. His effect can be used to Tribute itself, including Cyber Twin, even if Cyber Twin says it can only use the above Fusion Materials for its Fusion Summon, but The Light Hex Sealed can be used as a substitute, since it is being used for a Special Summon, but not a Fusion Summon. If you are talking about his substitute effect, I'm not sure how you even can use that effect without the use of Polymerization.
no, dragon master knight can only be fusion summoned.
No, Divine Wrath can only be used against effects that activate. Most of the time, when a monster has a way to special summon itself, this is an inherent special summon, just like a normal summon, it does not use the chain. Because it doesn't use the chain, you can't chain an effect negation card to it, though you can use summon negation cards like Solemn Judgment. If the special summon is an activated effect (like Dandylion's effect to special summon tokens, or Gorz's effect to summon himself) then these can be stopped using Divine Wrath. But Cyber Dragon's special summon cannot.