Macbeth could indeed be referring to Banquo obliquely in this scene as "the snake," when he says that they have "scorch'd the snake, not killed it." However, Macbeth's description of the snake as a still-living thing, which is still "herself, / whilst our poor malice / Remains in danger of her former tooth" indicates that Macbeth is thinking of something far bigger than Banquo when he speaks of "the snake." He is telling Lady Macbeth that they have only temporarily put off, "scorch'd," the threats to Macbeth's power. Banquo has not yet been killed; as Macbeth later says, "Thou know'st that Banquo, and his Fleance, lives." It is because of this that Macbeth describes his own mind as "full of scorpions."

There is a visual connection between the imagery of the snake and that of the scorpions: both are creatures generally associated with evil—particularly the snake, whose associations with the cunning snake (Satan) in the Garden of Eden are clear. The snake represents, thus, a threat to paradise, or the element which will bring down the carefully-constructed plan. In the same way, the "scorpions" in Macbeth's mind suggest that his mind is not at rest because the threat of intrusive thoughts, smaller reminders of the greater "snake," is always there.

When MacBeth exclaims "we have scorched the snake, not killed it" he is referring of course, to Banquo and also really anyone who is a threat to his power and his crown. He thinks of Banquo in this way because of the witches' prophecy that he will produce kings but not be one himself. MacBeth unjustifiably refers to Banquo like this because he has identified Banquo as a threat that could, as a snake can, lurk in the underbrush and strike him when he least expects it. It is an ironic use of the image, since it is MacBeth who really is the "snake."

I'm not sure if you have the correct lines for your final question. Are you referring to when MacBeth refers to his mind as being "full of scorpions"? Qualify the lines, then I can add further insights.