If the monster is a 'special summon only' monster, then it can be revived from the graveyard by cards like Monster Reborn, only if the monster was properly special summoned by the listed methods. Synchro, Ritual and Fusion monsters count, and are considered properly summoned when Synchro, Ritual or Fusion Summoned. In the case of Fusion Monsters who can't be Fusion Summoned (XYZ fusions, Gladiator Beast Gyzarus), then simply following the text is enough to count as properly summoning it. Examples of 'improperly' summoning them would by Cyber Stein, and Starlight Road, as these do not Fusion/Synchro Summon.
If the monster says 'cannot be special summoned except by', then there is no possible revival from the graveyard except in the most specific circumstances (Level Modulation), and even then, it must be properly summoned first.
Lastly, if the monster has neither restriction, then it does not need to be summoned properly first, these cards can be discarded and Monster Reborn'd freely.
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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. A Fusion Monster cannot be summoned from the graveyard unless it was properly special summoned first. Normally this would be Fusion Summon - the only exception are Fusion Monsters who can't be fusion summoned, like the Neos and XYZ fusions. All you need to do for those is follow their text, for them to be properly summoned. Either way, a Fusion Monster placed straight into the graveyard by Fusion Guard cannot ever be special summoned from the graveyard by any method.
No. Judgment Dragon says it 'cannot be special summoned except by...' and this way is the only way it can ever be special summoned. It cannot ever be revived from the graveyard by cards like Monster Reborn.
If a monster says "can only be special summoned by.." then if you summon it properly by this method, and it then goes to the graveyard, you can bring it back with Monster Reborn. If a monster says "cannot be special summoned except by.." then that's the only way it can ever be summoned. Even if you summon it properly first, it cannot be revived from the graveyard, except under the most extreme and specific circumstances (Level Modulation). Blue-Eyes Shining Dragon belongs to this latter group, so cannot be special summoned from the graveyard at all.
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.