You can make 1-2 gallon batches on the stove in a stock pot using a spaghetti strainer. I knew of a 70+ year old woman who would do just that.
Sure you can. But an interesting challenge is to adapt the standard batch size to accommodate the brewer, who might be a person with a bad back, undergoing chemo, wheelchair-bound, or for that matter pregnant (there must be women who have brewed while pregnant--after all, *making* beer isn't the problem), or is simply brewing in a challenging home environment--for example, where the ideal fermentation area is a steep flight of steps up or down from where brewing takes place.
(It interests me that 5 gallons *is* the de facto standard--why not 4 or 6? how did it come to be 5?--and if I ever get the time to research that question, I will.)