Is this an accurate introduction to different paths and traditions? The accepted answer to What teachings do all schools of Buddhism share? includes Compassion, the Triple Jewel, the Four Noble Truths, the Eight-fold Way, Dependent Origination, the Three Marks of Existence, the 37 Factors of Enlightenment, and more.

It also implies that Mahayana acknowledges one Path of Purification (visuddhi-marga):


Is that one Path the same (or basically the same) as The Visuddhimagga which Wikipedia says is "the 'great treatise' on Theravada Buddhist doctrine written by Buddhaghosa approximately in 430 CE in Sri Lanka"?


Furthermore, accepting that there's one "Path of Purification", the Wikipedia article titled "Buddhist Paths to liberation" seems to suggest that there's almost a different Path for each tradition.


Is this a reliable article?
Does it properly list the various schools/tradition and accurately summarize their paths?


When I've read elementary/contemporary/English-language introductions to various schools (e.g. Zen Flesh Zen Bones for zen), or visited a Chinese-in-Canada Mahayana temple, or dimly remember a Westerner writing a century or more ago about Tibetan/Mongolian beliefs and practices, they seem to have little in common with each other: e.g. Zen seems to be about being spontaneous or 'original', Chinese about things being better in the Pure Land, Tibetan about the cycle of rebirth.


Is it true, as stated in these Notes, that for all Buddhist traditions, the "Noble Eightfold Path is considered to be the essence of Buddhist practice"?


The article on Tibetan Buddhism begins, "Tibetan Buddhism comprises the teachings of the three vehicles of Buddhism: the Foundational Vehicle, Mahāyāna, and Vajrayāna" where 'Foundational Vehicle' links to the article on "Hinayana".


Do the practioners of various schools know, are they taught, what the Hinayana doctrine is, and do they accept it a "foundational"?
Is that one Path the same (or basically the same) as The Visuddhimagga
  which Wikipedia says is "the 'great treatise' on Theravada Buddhist
  doctrine written by Buddhaghosa approximately in 430 CE in Sri Lanka"?


The Visuddhimagga is the name of a book, and when traditions talk about a path of purification, they aren't using the term to refer to the title of this book, but just as a general term meaning a means of purification. I don't think that the other traditions even had access to the Visuddhimagga prior to modern times.


  When I've read elementary/contemporary/English-language introductions
  to various schools (e.g. Zen Flesh Zen Bones for zen), or visited a
  Chinese-in-Canada Mahayana temple, or dimly remember a Westerner
  writing a century or more ago about Tibetan/Mongolian beliefs and
  practices, they seem to have little in common with each other: e.g.
  Zen seems to be about being spontaneous or 'original', Chinese about
  things being better in the Pure Land, Tibetan about the cycle of
  rebirth.


All of these traditions are very vast systems of teaching and practice, and they all use very different terminology, and some traditions emphasize certain points while others might not emphasize a particular point, but that doesn't mean that they reject them. Just because these teachings are held in common between all traditions doesn't mean that they describe them using the same terms, or even teach them in an explicit manner. Take Zen Buddhism for example. For the past 1000 years, the main slogan of the Zen school has been "See mind, become Buddha" meaning that the practice is to see the nature of the mind and as a result one becomes enlightened. This terminology is very different from how the Theravada tradition would describe it, as the Theravada school would give a quote like this:


  "What do you think, monks — Is form constant or inconstant?"
  
  "Inconstant, lord."
  
  "And is that which is inconstant easeful or stressful?"
  
  "Stressful, lord."
  
  "And is it fitting to regard what is inconstant, stressful, subject to
  change as: 'This is mine. This is my self. This is what I am'?"
  
  "No, lord."
  
  ...
  
  Seeing thus, the well-instructed disciple of the noble ones grows
  disenchanted with form, disenchanted with feeling, disenchanted with
  perception, disenchanted with fabrications, disenchanted with
  consciousness. Disenchanted, he becomes dispassionate. Through
  dispassion, he is fully released. With full release, there is the
  knowledge, 'Fully released.' He discerns that 'Birth is ended, the
  holy life fulfilled, the task done. There is nothing further for this
  world.


But this difference of expression doesn't preclude the existence of things in common. Both of these explanations present enlightenment as the result of seeing the nature of something, even though the language and style may be very different. Tibetan Buddhism holds to the same position as well, saying that enlightenment results from gaining a non-conceptual realization of the emptiness of all phenomena. Pureland Buddhism hold on to these teachings as well, but sees the appropriate time for actually practicing such things to be after one is reborn into the Pureland, and even that is only one interpretation of Pureland Buddhism. Chinese Buddhism fuses Zen and Pureland practices together for example.

There are real differences between the traditions, I'm not saying that there aren't. However, all schools of Buddhism hold on to this set of common teachings, even though they differ in their interpretations and their importance.