Not unless the special summoning effect specifically says you can, like The Shallow Grave does.
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Not if you normal summon. if you special summon, then yes.
No, a Tribute Summon follows the same position rules as a Normal Summon, so a monster you Tribute Summon is either face-up attack or Tribute Set into face-down defense.
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.
Yes, the tributed monster does not have to be face-up at all, it can be tributed while face-down.
Setting is similar, yet not identical to normal summoning. a normal summon is when you Summon a monster onto the field in face-up attack position, whereas a set is when you normal summon a monster in face-down defense position. When a monster is set, it is not yet considered a summoned monster.