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.
Yes, Machina Fortress can be discarded as part of the cost for its own effect, and then that same Machina Fortress can be special summoned from the graveyard.
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.
No, unless specifically stated otherwise on the card, a monster's special summon requires it to be summoned from your hand, or in the case of Synchro and XYZ monsters, from the Extra Deck.Plaguespreader Zombie can special summon itself from the graveyard because it says it can. But you cannot use for example, the special summon requirements on Chaos Sorcerer, or an XYZ monster, while they are in the graveyard.
If you properly Special Summoned him first, and he is then destroyed, you can special summon him back from the graveyard with cards like Monster Reborn. You do not need to remove another Light and Dark monster to do this, and just as important, you cannot remove a Light and Dark monster to special summon him from the graveyard, he can only be summoned from hand by doing that.
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.
His initial special summon must be from hand, using the text on his card. If you do this correctly, and he then goes to the graveyard, you can special summon him back to the field with cards like Call of the Haunted. If however the summon is negated, or he is simply discarded to the graveyard, you cannot special summon him from the graveyard by any means. Nor can an external effect special summon him from hand, it must be his own.
Special Summoning from the Graveyard requires an effect that specifically allows you to do so. Call of the Haunted, as an example, allows a player to select and Special Summon one monster from their respective Graveyard in face-up Attack Position.
when you discard a card for Vampire Genesis' effect, that card is treated like any other card in the graveyard. It means that if that card is taken out of the graveyard the special summoned monster is not affected since there is nothing binding the two. simply put it's just a cost to special summon. you can use the discarded card as you would any other card in the graveyard.
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.
The 'Chaos' monsters - Chaos Sorcerer, Chaos Emperor Dragon Envoy of the End, and Black Luster Soldier Envoy of the Beginning must be special summoned initially from hand by removing from play 1 light and 1 dark monster in you graveyard from play. Once you do this, after the monster is destroyed and goes to the graveyard, you can then resummon it using cards like Monster Reborn.
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.
Special summon Quickdraw Synchron discarding Level Eater, special summon Level Eater from the graveyard, then sync them. Level Eater -- 1 star If this card is in the Graveyard, you can activate its effect by selecting 1 face-up Level 5 or higher monster you control. Reduce that monster's Level by 1. Special Summon this card from the Graveyard. This card cannot be Tributed except for a Tribute Summon. Quickdraw Synchron -- 5 star You can send 1 monster from your hand to the Graveyard and Special Summon this card from your hand. You can substitute this card for any 1 "Synchron" Tuner for a Synchro Summon. This card cannot be used as a Synchro Material Monster, except for the Synchro Summon of a monster that lists a "Synchron" monster as a Tuner monster.