No, the monster is not being summoned in any way, all that is happening is that its controller changed.
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Basically, when you special summon a monster with 1500 or less ATK with cards like marauding captain, call of the haunted, or monster reborn, you can activate this card when your opponent has a face-up monster to special summon all copies of that monster. Your opponent can special summon all copies of his monster too, but that's a rare chance IMO.
Unless stated otherwise (Plaguespreader Zombie for example) a monster's special summon is done from hand only. Lava Golem must be in your hand, for you to be able to special summon it using the listed text on the card.
Call of the Haunted special summons on resolution. If this resolution is negated, then it will not special summon anything. Even if the negation effect stops being applied later on, Call will not then summon a monster.
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.
Yes, a Special Summon of any kind does not count towards your limit of one Normal Summon or Set per turn. You can Special Summon as many times a s you want per turn.