yes it can
As is stated on his card, his trigger to special summon two Gladiator Beast cards can only be activated if he himself was special summoned by the effect of another Gladiator Beast. If he was just Normal Summoned or special summoned by a card like Monster Reborn, then his effect will not trigger after he attacks or is attacked.
im guessing gladiator beast im not sure though
Because it is an 'only be special summoned by..' monster, that means it can be special summoned by cards like Monster Reborn, after it was summoned properly but was destroyed. Note that a field spell card is in no way part of Malefic Blue-Eyes White Dragon's summon condition. MB-EWD will simply be destroyed if it is ever face-up on the field, and no Field Spell Card is in play. So if Monster Reborn was used in this case, MB-EWD would be special summoned, and then destroy itself.
Vampire Genesis 'cannot be special summoned' except by following the instructions on the card. If a monster says it can 'only' be special summoned a certain way, this is for the initial summon only. If you summon it properly, and it is destroyed, then you can revive it from the graveyard with Monster Reborn. However the 'except by' monsters can't be special summoned by any other means than the text on their card. Even if they are properly special summoned first, you still can't use Monster Reborn on them.
The Deck is shuffled whenever something is 'returned to' it, or removed due to a search effect. Yes, it must be shuffled after another Gladiator Beast is Special Summoned on resolution.
No, monsters can only be normal or special summoned to the monster card zone. Crystal Beasts go to the S/T zone when destroyed, you don't place them there automatically.
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.
You can tribute a special summoned monster, yes.
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.
Yeah. There's just two kinds of monsters you need to look out for; 1 - Monsters that say "Can only be special summoned by..." These monsters have to be summoned properly by their own effects first, if you wish to use Monster Reborn on them. You can't just discard them and use Monster Reborn. 2 - Monsters that say "Cannot be special summoned except by.." The only way (barring a few highly specialised circumstances) these can ever reach the field, is by following their own text. They cannot be special summoned from the graveyard by Monster Reborn, even if they were properly summoned first.
A monster's special summon text only applies while it is in your hand. If a monster says it can 'only be' special summoned by a certain method, then assuming you do summon it properly, and it is then destroyed, then you are allowed to use Monster Reborn and do not have to pay any additional costs. If the above monster was simply discarded from hand by something else, then it can not be special summoned by Monster Reborn. If it says 'cannot be special summoned except by..' then it can't be brought back with Monster Reborn even if it was properly special summoned first.
"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.