You can attack your opponent's face-down monsters. You cannot attack his face-down S/T cards though.
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Only the Spell card Darkness Approaches can flip a monster into face-down Attack position. By discarding two cards, Darkness Approaches lets you flip one face-up monster face-down without changing the battle position (so a monster may end up in face-down Attack position).
A monster in face-down Attack position is unable to declare attacks. It can be flipped or Flip Summoned, both actions will switch it into face-up Attack position. It can also have its battle position change by the controlling player, switching it from face-down Attack position to face-down Defence position.
Yes. It doesn't matter if the Wall of Illusion is face-down when the attack was declared.
A monster can't manually change battle position on the turn it declared an attack, but it can still be flipped face-down by an effect. Golem Sentry can attack, then activate its effect in main phase 2 and flip itself face down.
'Negate' is a very specific word in Yu-Gi-Oh. No, Interdimensional Matter Transporter does not 'negate' the attack (unlike cards such as Necro Gardna), but the attack is stopped nonetheless. As soon as the attacking monster leaves the field, that particular attack step ends, the defending monster is not flipped if face-down, and no damage is calculated.