Yes - I'd call a hot dog a sandwich, though most folks refer to it as a special category all its own. It's bread enclosing meat (etc.), you can tote the entire item around as a single object, and it's eaten by hand rather than by implement.
No - I wouldn't consider (cold) cereal with milk a soup. For one thing, its ingredients are combined in the final moments before consumption, whereas soups (even those served cold, in my experience ... ) have their ingredients combined and collectively steeped prior to serving.
I suppose I consider the relationship between cereal versus soup to be akin to the relationship between a mixture and a compound in chemistry. I see cereal as a mixture of at least two components whose individual characteristics remain evident, whereas I see soup as a compound (blended / joint composite) of the initial ingredients.
I can eat cereal dry, drink some milk separately, and claim with no more than a mischievous smirk that I've 'eaten cereal'. I can't separately eat (e.g.) carrots, peas, chicken, etc., and claim I've eaten chicken soup.
Furthermore (and just in case ...), I'd have a hard time referring to hot cereal (e.g., oatmeal) as anything approximating a soup, though I concede it can be quite 'soupy'.