Yes, it will be unaffected by the effects of any and all types of spells, whether they be Normal, Quick, Field, Continuous or Equip. The Legendary Fisherman for example gains protective effects if Umi is in play, however it therefore becomes immune to Umi's effect and doesn't gain the ATK bonus it would normally grant.
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Monsters who go into the S/T zone for any reason are then treated as Continuous Spell Cards or Equip Spell Cards depending on what it is doing. It is no longer a monster card so is unaffected by anything that specifically affects monster cards, and cannot be tributed for a tribute summon, etc. However if something required you to send an Equip Spell Card to the graveyard, you could use that monster.
A card you 'control' is something on your side of the field, be it a monster, spell or trap, and it can be something the opponent owns, but you've taken control of by whatever means.
No. A monster like Elemental HERO Wildheart cannot have its attack negated by Negate Attack, and because the attack was not negated, the battle phase will not end either.
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If they are Summoned as Normal Monsters, they are unaffected. If they are Summoned as Effect Monsters, they will be moved face-up into the S/T zone and cease to be monsters while Skill Drain is active. Even if Skill Drain is removed from the field, they will not return to the monster zone, they will remain uselessly in the S/T zone.