A Fusion Summon is a Special Summon and things that can be used against Special Summons can also be used against a Fusion Summon.
But not all Special Summons are Fusion Summons, even if they do so happen to summon a Fusion Monster. For example, Cyber Stein Special Summons a fusion monster, it does not Fusion Summon it.
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Yes, of course. You are allowed to perform as many special summons in a turn as you've got the resources to do so, Synchro and Fusion summons are kinds of special summon.
No, Elemental Hero Dark Gaia cannot be special summoned, except by the effect of 'Dark Fusion'. You cannot use any other special summon methods (like Monster Reborn), or even other fusion summon methods (Polymerization, Re-Fusion, Future Fusion).
A Fusion Monster can never be Normal Summoned, as it is impossible to put them in your hand. A Fusion Monster must be Special Summoned, be it Fusion Summon through Polymerization or similar, or a regular Special Summon by any card that can do it.
Cyberdark Dragon cannot be summoned except by Fusion Summon. Cyber Stein does not 'fusion summon' the fusion monsters is summons, it is only a special summon. It therefore cannot summon monsters like Dark Paladin, or Cyberdark Dragon.
A Fusion Summon, or the Summoning of any Monster (Synchro or Fusion) from the Fusion Deck (Extra Deck) is a special summon and so Trap Hole will not work on it.