Time is relevant, as "order" on a cladogram is chronological order. It's a historical narrative. For a better understanding of cladograms and why there are competing ones, try a Workshop on Biosystematics.
More on cladistic principles in Character Analysis. It's a narrative constructed entirely from character traits themselves. The results tend to correlate to a with the observed appearances in the fossil record. Nevertheless, it's not unthinkable that that they won't always. The fault may be suspected in the fossil record, but the cladogram isn't gospel. In fact, the links were obtained by a Yahoo! on "competing cladograms." Note that the fossil record is viewed as an interesting external test for evaluating dueling cladograms.
No it is not! In the case we are discussing the "feather" evidence is placed ~22 million years prior to the dating of the fossil bearing that evidence.