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Yes, Darksteel Colossus would stay dead.
Darksteel Colossus has a replacement effect that modifies how it goes from any zone to the graveyard. If it's a creature and is targeted by Snakeform , it will stop being a Darksteel Colossus creature until the end of the turn; Instead, it will be a 1/1 green Snake with no abilities. If that snake is put into a graveyard nothing will happen, as it's a snake that died.
The card that ends up in your graveyard will be the Darksteel Colossus, but since it was something else at the time it transitioned there its ability won't exist to replace the movement.
BrightGreenLine is right. A replacement effect has to exist before the event it would apply to, and the Snake on the battlefield doesn't have the Colossus' graveyard-avoiding ability, so there's no effect to apply before it goes to the graveyard.
Changing the card's name doesn't do anything if you don't also take away the associated ability. When a card uses its own name in its text, it really means "this card right here", and will continue to refer to the card regardless of what happens to its name. For example, Sakashima the Impostor pretending to be Darksteel Colossus will shuffle itself back into the library if it would die, because the ability copied from the Colossus is referring to the Sakashima card.
Sure, no problem. The following rule quote is from the Comprehensive Rules (the examples beneath it are also from the Comprehensive Rules):
201.4b If an ability of an object refers to that object by name, and an object with a different name gains that ability, all instances of the first name in the gained ability should be treated as the second name.
Example: Quicksilver Elemental says, in part, "U: Quicksilver Elemental gains all activated abilities of target creature until end of turn." If it gains an ability that says "B: Regenerate Drudge Skeletons ," activating that ability will regenerate Quicksilver Elemental, not the Drudge Skeletons it gained the ability from.
Example: Glacial Ray is an instant with "splice onto Arcane" that says "Glacial Ray deals 2 damage to target creature or player." If it's spliced onto a card:Kodama's Reach, that Kodama's Reach deals 2 damage to the target creature or player.
Example: Dimir Doppelganger says "1UB: Exile target creature card from a graveyard. Dimir Doppelganger becomes a copy of that card and gains this ability." Dimir Doppelganger's ability is activated targeting a Runeclaw Bear card. The Doppelganger becomes a copy of Runeclaw Bear and gains an ability that should be treated as saying "1UB: Exile target creature card from a graveyard. Runeclaw Bear becomes a copy of that card and gains this ability."