Of course. There is nothing about being tapped that stops a creature being targeted or otherwise affected by a spell or ability, unless specifically stated that they work only on untapped creatures.
No, creatures with summoning sickness cannot be tapped in Magic: The Gathering.
Creatures are not brought into play tapped, but they have summoning sickness preventing them from tapping to attack or to tap to activate any abilities unless they have the keyword "haste".
Yes, you can regenerate a tapped creature in Magic: The Gathering by paying the regeneration cost, even if the creature is tapped. Regeneration prevents the creature from being destroyed the next time it would be destroyed that turn.
You choose a player to use it on when you cast it. When it resolves, tap all their creatures. When that player next has an untap step, he may not untap any of these creatures. A creature played and tapped after Sleep resolved, may untap in the next untap step. However a creature that was already tapped before Sleep resolved, may not untap. That's because Sleep's effect was applied to it (it affects all their creatures, not just untapped ones), even though it could not physically become tapped by Sleep.
No, they do not. It would not affect them in any way though, the only Planeswalker affected by tapping is Gideon Jura.
No, note it says 'Untap target nonlegendary creature", not "Untap target tapped nonlegendary creature." Most of the spells that steal control like this, will allow you to untap the creature if it's tapped. But they're all still fine to be used against creatures that are originally untapped too.
In Magic: The Gathering, creatures entering the battlefield must follow certain rules. They typically enter tapped unless a card effect says otherwise. They can't attack or use abilities that require tapping on the turn they enter unless they have haste. They also trigger "enter the battlefield" abilities when they come into play.
In Magic: The Gathering, when a creature is regenerated, it means that if it would be destroyed, it instead becomes tapped and removed from combat. This allows the creature to survive the destruction effect. Regeneration typically requires the payment of a specific cost, such as mana or tapping the creature itself.
Creatures cannot be 'attacked' in Magic the Gathering. Players are attacked, and creatures are declared as blockers, although there are a few special abilities that can force things to attack or block. A tapped Planeswalker can be attacked, as per the usual rules for declaring attacks against Planewalker cards. Targeting a creature with a damage dealing spell or ability is not 'attacking' them. The creature being tapped has nothing to do with its targeting eligibility, it can still be targeted by cards that deal damage. Damage spells never target Planewalkers directly, the cards target the controlling player and the damage redirected to the Planeswalker from there. This can be done to a tapped Planeswalker.
no
No, "Island" is not a spell in Magic: The Gathering. It is a basic land card that produces blue mana when tapped.
Convoke allows players to tap creatures to help pay for the mana cost of a spell. Creatures tapped this way cannot attack or use abilities that require tapping until the next turn, due to summoning sickness. This can impact the immediate board state and strategy of the player.