No, you can't unless the card says so
No, the text for Cyberdark Dragon says: "This monster cannot be Special Summoned except by Fusion Summon..."
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.
No. If a monster says it 'cannot be special summoned except by', then the listed method is the only way it can reach the field. By default, this summon is from the hand too. So, even if you properly special summon Dark Armed Dragon, and it goes to the graveyard, you cannot special summon it using either its own special summon effect, or the effect of cards like Monster Reborn.
Unless stated otherwise, a card's special summon requirement is from the hand only. Rainbow Dark Dragon can't be special summoned except from hand, by removing the seven differently name Dark monsters from the graveyard.
You can perform as many special summons per turn as you are able to, as well as your one Normal Summon and any Flip Summons.
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, unless stated otherwise, a monster special summon effect works from the hand. Treeborn Frog special summons itself from the graveyard, because it says so. DD Survivor special summons itself from the removed from play zone, etc. But Dark Armed Dragon can only special summon itself from hand.
No. Grapha, Dragon Lord of Dark World's inherent special summon can only be used on your own turn. Only monsters who summon themselves by a Triggered Effect, or by Quick Effect, or specifically say they can be summoned on the opponent's turn, can do otherwise.
Removing a Light and Dark monster can only special summon a Chaos Emperor Dragon from your own hand. When it's anywhere else, you can't remove another Light and Dark to summon it. If you summoned it properly, you can resummon it with Monster Reborn though.
No, Berserk Dragon cannot be special summoned except by "A Deal with Dark Ruler". No external effect can get around this, that is the only way it can hit the field.
yes
No. Unless specifically stated otherwise, a card's special summon text is to summon it from the hand only. Chaos Emperor Dragon requires the owner to remove one Light and one Dark monster to summon it from his hand, but it cannot be done while it is in the graveyard, and especially, the opponent cannot do it.