Yes, you can. Unless the card lore specifically states "...tribute one face-up [monster name]..." you can automatically assume that you can tribute it face-down. However, you must reveal to your opponent that the face-down monster is in fact Levia-Dragon - Daedalus before tributing it.
Yes because it's effect says you can summon a normal dragon type monster from either players graveyard. So since tribute to the doom destroys the monster is effect activates.
Yes. Hardened Armed Dragon doesn't need to be face-up. The effect is not on that activates, it's just something that's checked after the tribute is paid.
Yes. Face-down monsters can be tributed for tribute summons, card effects, etc.
Of course not. Red-Eyes Black Chick offers a slightly easier way to get a Red-Eyes Black Dragon in play. However, Red-Eyes Black Dragon is still a Normal Lv7 monster and as such can be tribute summoned by offering two monsters as tribute as normal, or any other method such as discard/revival with Monster Reborn.
Yes, monsters may be 'tribute set'.
Paladin of White Dragon can only be be summoned with the Ritual Spell Card White Dragon Ritual and the tribute of monsters whose total levels equal 4 or more from the field or your hand.When this monster attacks a face-down defense position monster, destroy that monster without flipping it face-up or calculating damage calculation. You can tribute this card to Special Summon 1 Blue-Eyes White Dragon from your hand or deck. (Blue-Eyes White Dragon can't attack during the turn it's summoned by this effect.)
The song Puff the Magic Dragon really talks about a Magic Dragon that lives down under inside a cave alongside the ocean. It really isn't about drugs.
Yes, you can.
If you are talking about the dragon on red dragon island: The dragon will be burning the houses down. So your dragon will have to put the fire out. And if you are to late, the houses will burn down and disappear.
Yes
Yes, the tributed monster does not have to be face-up at all, it can be tributed while face-down.
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.