Rank-specific rules for taxonomic classification
In short, no. Species are unique, in that they are thought to be biologically real categories that would exist whether there were humans trying to classify them or not. There are a variety of definitions for species, involving fixed characters that imply a lack of gene-flow. However, all higher categories, from genera on up are designed by humans to be able to talk about these groups. Each category is defined by phylogenetic relationships, but taxonomists have wide leeway to decide how broadly or narrowly to subdivide groups. (Lumpers vs. Splitters). For example, all ants are in the same family. Yet all it would take to change this would be for some ant taxonomist to submit a paper that divided ants into however many families s/he wanted to. The peer reviewers would then decide if such a division was reasonable, and once published, it would be the new taxonomy. There are no broad rules, other than peer review. Not age: one family could be 1 million years old, and another, 100 million. Not the magnitude of phenotypic or genotypic variation: some groups are radically different from one-another, and still in the same category, while other groups are heavily subdivided and barely distinguishable.