Assuming one's character is 1 foot or smaller (either naturally or through some other ability, e.g. Alter Self), and then use Disguise Self to [...] seem 1 foot shorter [...], would this character effectively disappear?
As an illusion, it would not change the physical aspect (the character would still exist in the same 3D space), just how the character is perceived. But other than that, how close of invisibility would that be?
Socially, how would you handle that situation - like an invisible character?
In combat, what advantage would this gives? Full cover? Advantage on attack and/or defense? Sneak attack?
Change Appearance. You transform your appearance. You decide what you look like, including your height, weight, facial features, sound of your voice, hair length, coloration, and distinguishing characteristics, if any.
Disguise Self: https://roll20.net/compendium/dnd5e/Disguise%20Self#content
You can seem 1 foot shorter or taller and can appear thin, fat, or in between.
When you attack a target that you can't see, you have disadvantage on the attack roll.
When a creature can't see you, you have advantage on attack rolls against it.