There appears to be a very specific (although not universally agreed) list of characteristics that describe what a "species" is--and the list applies to ALL species. Are there similar generic rules or characteristics for the other taxonomic ranks that do not resort to characteristics of existing members of the rank? For example, I've seen "number of lobes on leaves" used to place a particular flower in a particular Family or Order. Is there anything that applies across ALL Families, or across ALL Orders, etc., of the tree of life?
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.
I agree that the overall answer is "no, there aren't consistent standards for what constitutes a taxonomic level". Perhaps someday we'll be able to say that an animal phylum denotes X years of divergence or Y amount of sequence similarity, but making those same judgements for extinct organisms or microbes is a lot messier. See Wikipedia on bacterial phyla for an example of how taxonomists are still debating whether bacteria should be said to have phyla at all, or whether they're more like kingdoms, or whether we should just use a different word entirely.
However, at the detailed level of one taxon here and one taxon there, evolutionary biologists and taxonomists can work toward greater local consistency. If it's discovered that species X is very different from the other species in its genus, and indeed it's as evolutionarily distant from them as the species in other genera are, then there's a reasonable argument for it to be "promoted" into its own genus. Other taxonomists working on the same group of organisms can choose to use that change as a precedent; and when people revise entire trees at the family or order level, they may be able to apply roughly the same standard throughout. It would be nice to think that through such processes we'll start creeping toward some sort of overall consistency; but I don't think it's likely to happen any time soon across kingdom- or domain-level barriers.