1) Yes, you can bring back the same Colossal Fighter.
2) You cannot, but I don't know the exact reasoning because the site explaining it was in japanese.
3) It's still considered to "Have Battled" so, say, if a Gladiator Beast Monster attacks Directly, it still gets the option to return to the deck.
4) You cannot activate gemini spark if you have no monsters, as the tributing is a cost.
5) if Amulet of Ambition is not equipped to a normal monster, it is destroyed immediately, so it's not considered to be "on the field" anymore.