The monster will always return to its owner's Graveyard.
Incidentally, if the effect of the destroyed monster activates while it is still on the field, you will be able to use it; however, if the effect activates in the Graveyard, the card's owner will control the effect.
Yes you can, as long as the Stardust was originally summoned by Synchro Summon and not by Starlight Road (Starlight Road does not summon it 'properly', and the Stardust Dragon summoned by it cannot be summoned back from the graveyard should it be sent there).
"The Rock Spirit" can only be Special Summoned from the Graveyard, if it was Special Summoned from the Hand via its effect first. In other words, if it was "improperly" sent to the Graveyard, such as by discarding from the Hand, it cannot be Special Summoned from the Graveyard. If it was successfully Special Summoned by its own effect onto the field and is then sent to the Graveyard, it is then elligible to be Special Summoned from the same Graveyard. However, if it's Special Summon was negated by a card effect such as "Solemn Judgment" and sent to the Graveyard, it cannot be Special Summoned from the Graveyard.
When a non-effect monster destroys another monster the destroyed monster is sent to the grave, unless there is another card on the field which changes where destroyed monsters go. Depending on the effect of the monster that destroyed them they are either sent to the Graveyard, are banished, return to the owners hand, or can be summoned on the opponents side of the field. Some cards can even be saved from the grave by their own effect and are then either re-summoned or go to spell/trap zone. Spell/trap cards can also determine where they go, as they can change it so that any destroyed monster is banished instead of being sent to the graveyard.
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.
Chaos Sorcerer must be initially summoned from hand. You cannot use his own special summon effect from any other location, like the graveyard. However, if he is properly special summoned by this method, and then destroyed, you are allowed to special summon him from the graveyard using cards like Monster Reborn. Monsters who say "can only be special summoned by..." all work like this, but ones who say "cannot be special summoned except by.." can't use any other method but their own. Lastly, if he's in the graveyard but was not properly summoned (like, his summon was negated, or he was simply discarded there) you can't use Monster Reborn on him.
If Herald of Perfection is successfully Ritual Summoned and is sent to the Graveyard, it is then eligible to be Special Summoned from the Graveyard, unless specifically denied by another card effect.
No, only from your hand. They can be special summoned from graveyard by cards like Monster Reborn if they were properly summoned initially before they went there. However you can't resummon them from the graveyard with their Ritual Spell Card.
Destiny Hero Dogma cannot be special summoned, except from in hand, by tributing three monsters. As an 'except by' monster, that means the listed method is the only way he can ever be summoned. He cannot be summoned by any other means, even if he was properly summoned first and then went to the graveyard.
Ritual monsters may only be special summoned from the graveyard if they were successfully summoned by Ritual Summon. If they were sent there in any other way - like simply discarded from hand, or improperly summoned by Ritual Foregone (it special summons but does not Ritual Summon), then you cannot revive them from the graveyard with cards like Monster Reborn or Fulfillment of the Contract.
Raviel's own special summon effect can only be used while he is in the hand.If he goes to the graveyard, he can't be special summoned. He can't be special summoned 'except' by through his effect while he is in hand.
No, because it wasn't 'properly' special summoned. To be able to special summon a Ritual Monster from the graveyard, it has to be initially summoned by Ritual Summon. Ritual Foregone does not Ritual Summon.
Cards which are special summon-only (ie, say 'can only be special summoned by' or 'cannot be special summoned except by') can not be simply discarded to the graveyard and summoned. 'Can only be special summoned by' monsters can be special summoned from the graveyard if they were properly summoned initially by the text on their card, before they ended up going to the graveyard. A note though, you resummon them with cards like Call of the Haunted, you can't use their own text again, that's for when they are in the hand only, unless specifically stated otherwise. 'Cannot be special summoned except by' generally cards can't be resummoned from the graveyard at all even if they were properly summoned first. There are one or two cards that can summon them, but they all specifically say they can do this - like Level Modulation - and still, the monster must have been summoned properly first.