You can't. It says in its text "This card can not be special summoned."
Light and Darkness Dragon will be switched into defense position. There is otherwise no interaction.
Yes. Summoning Chaos Sorcerer is not an activation unlike the Triggered effects of Gorz or Battle Fader. It does not use the chain, just like Normal Summons. So Light and Darkness Dragon has no interaction with it.
Light Pulsar Dragon's effect allows you to Special Summon a Dragon-type monster from your Graveyard when it is Special Summoned. This effect can only be used once per turn. Additionally, if Light Pulsar Dragon is sent from the field to the Graveyard, you can Special Summon a DARK Dragon-type monster from your Graveyard.
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. 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.
Light and Darkness Dragon's first line of text says that it cannot be special summoned. Therefore when it is destroyed and its last effect triggers, it cannot choose itself.
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.
A monster's special summon method can only be used while the monster is in your hand - unless stated otherwise. You can't simply summon monsters like Cyber Dragon or Andro Sphinx straight from deck through their own summoning conditions, they must be in your hand.
Storm Of Ragnorark
a good strategy for light and darkness dragon is to include counter traps, because its effect cannot negate them. you could also try a beat down strategy where you negate your opponents card effects with light and darkness and attack for win.
Blue-Eyes Shining Dragon cannot be special summoned except by tributing a Blue-Eyes Ultimate Dragon. There is simply no way around it. The Hex-Sealed Fusions are 'fusion substitutes' meaning they can take the place of a fusion component for a Fusion Summon. You may use The Light and two Blue-Eyes White Dragons to summon Blue-Eyes Ultimate Dragon, but apart from that, it has no way to combo with Shining Dragon at all.
Light and Darkness dragon is better pretty much no matter what. Unless you're running Crystal Beasts.