Your sentences are grammatically correct but a more natural way to say it would be: Я спущусь за баночкой колы для вас or Я спущусь, принесу вам баночку колы or Я схожу за баночкой колы для вас. Although "downstairs " and "upstairs " imply that there are "stairs " where you are, we often omit the word лестница. Instead, we use the verbs that describe a movement up or down, that is "спуститься" = go downstairs and "подняться" = go upstairs. By the way, your sentences make me think of an informal meeting or party and , perhaps, you might say для тебя rather than для вас. :)

Я пойду вниз по лестнице, чтобы взять тебе баночку кока-колы. This grammatical structure of sentence is correct.

All of these sentences are correct, but they sound a little strange. It's better to say like this - Я спущусь вниз за банкой колы для тебя. The word 'лестница' is not pronounced, because it is already clear.