Phylogenetics and the Tree of Life
Let's start with a short comment. You say [..]evolution is nowadays pretty much analyzed through phylogenetic trees[..]. Many evolutionary biologist make extensive use of phylogenetic methods but a good part of evolutionary biologist (most of them I would say) do not work directly with phylogenetic methods.



I am not sure I understand your question but I hope the following may help you either to understand the issue or to edit your question. Note that I am NOT a phylogeneticist (not sure this word exist).

What is the definition of "Node" in Phylogenetics

I think your definition of a node might be unusual. In phylogeny, a node is the most recent common ancestor shared by two sister lineages.

Time in a phylogenetic tree

Also, when you look at a phylogenetic tree, the axis along which lineages diversify represent the time (real time in years). Now, we use different methods in order to make estimation of this real time such as the rate of neutral substitutions. You may want to read about molecular clock


  each successive node has taken time to develop?


I am not sure what you mean by "develop" here. Develop usually means the process by which a given individual/organism change phenotypically through its lifetime. See Developmental Biology.


  average time it takes for any organism to loose or acquire a certain trait


Again, I am not sure whether you talk about development or evolution here as you talk about "any organism" and not about "any population". In any case, an average time for a population to acquire a given arbitrary trait is a concept that 1) is valid only for discrete trait, 2) that is very dependent on the kind of trait you want to consider, 3) that will varies a lot from one given trait to another and 4) is extremely dependent on when you consider being the starting point of the evolutionary process toward the creation of the given trait. Therefore, it doesn't makes much sense.

Currently used "standard evolutionary time unit"

However, you can use similar concept for quantitative traits. The Darwin (d) is a unit of evolutionary change (invented by Haldane and named after C. Darwin). It is defined as the e-fold (e≈2.7) in a mean of individual's trait in a population over million of years.

Similarly, the Haldane is a unit of evolutionary change (I don't know who invented it and it is obviously named after JBS Haldane) and correspond to the number of standard deviation (of the distribution of individual trait in the population) change in the mean of individuals trait in a population per generation. The Haldane unit is therefore dependent on the selection pressure, the additive and non-additive genetic variance and environmental variance (therefore the heritability) and the mutational pressures.