Did Manjushri, Vajrassatva, Avalokiteshvara live? Did Manjushri, Vajrassatva or Avalokiteshvara live? 

Are Manjushri, Vajrassatva or Avalokiteshvara manifestations or special names of Buddhas or Bodhisattva?
Vajrasattva did not live in the sense you mean, because he is not a person, but he is an existent. I will explain further:

The form body (Rupakaya), is divided in two:


The emanation body (Nirmanakaya), and
The enjoyment body (Sambhogakāya)


From a Tibetan viewpoint, Shakyamuni was an emanation body of the Buddha. He merely showed the aspect of being born, aging, achieving enlightenment, passing into parinirvana, and so forth [but was actually free from birth, aging, sickness and death and so forth]. While the enjoyment body is too subtle for ordinary beings to see, the emanation body is seen by ordinary beings. Wheel-turning buddhas are thus said to be emanation bodies.

Vajrasattva, on the other hand, would be the enjoyment body in the aspect of a Bodhisattva. Such a body can be seen by arya beings. We claim that when an arya bodhisattva chooses to be reborn in a pure land in order to receive teachings there from other bodhisattvas, he receives teachings from actual bodhisattvas as well as from the enjoyement body in the aspect of bodhisattvas (such as Vajrasattva, Manjushri, and so forth). Vajrasattva is one of these aspects, manifestations. He is a subtle manifestation of the form body of buddha.

Avalokiteshvara was one of 'the eight principal Mahayana disciples of Buddha Shakyamuni', that is the sambhogakaya in the aspect of a disciple. The same is true of Manjushri. The main difference between Manjushri and Vajrasattva, in relation to their entity, is that Manjushri is said to be a [manifestation of the] wisdom truth body (i.e. the omniscient mind) and not that of the enjoyment body.