Short answers, pulled from the story.
Avalokitesvara means "lord who gazed down at the world", combining the Sanskrit prefix ava ("down"), the verb lok ("to look, notice, behold, observe"), and isvara ("lord" or "ruler"). The word for world, loka, is implied by the phrase rather than present in the name itself, though it appears in the Cambodian form Lokesvarak.
Guanyin is the East Asian female form of Avalokitesvara, the bodhisattva of compassion. The name Guanyin means "perceiving sound" or "hearing the world's cries" and reflects an earlier Sanskrit form of the name, Avalokitasvara. Depicted as a divine mother in a white robe, Guanyin is worshipped across Chinese Buddhism, Taoism, and Chinese folk religion.
According to Buddhist tradition, Avalokitesvara vowed never to rest until all sentient beings were freed from suffering. When his head split from the strain of comprehending so many beings in need, Amitabha Buddha gave him eleven heads to hear all their cries. When his two arms shattered as he tried to reach everyone, Amitabha gave him a thousand arms to aid the multitudes.
Om Mani Padme Hum is a six-syllable mantra that is the most popular mantra in Tibetan Buddhism, and its connection to Avalokitesvara is first documented in a sutra dated to approximately the late 4th to early 5th century CE. Because of this association, one form of Avalokitesvara is called Sadaksari, meaning "Lord of the Six Syllables". Reciting it while spinning a prayer wheel clockwise is among the most common religious practices in Tibetan Buddhism.
In Sri Lanka, Avalokitesvara is worshipped as Natha-deva. Most worshippers believe Natha to be Maitreya, the future Buddha, but scholars identify the figure as Avalokitesvara based on iconographic evidence, including an image of Amitabha Buddha on the front of the crown. Andrew Skilton noted that this evidence implies a broader Mahayana presence in Sri Lankan religious history than is commonly acknowledged.
The Karandavyuhasuttra, dated to the 4th-5th century CE, states that major Hindu deities including Vishnu, Shiva, Brahma, and Saraswati all emerged from specific parts of Avalokitesvara's body. However, scholars note that this portrayal does not make Avalokitesvara a Creator God in the Hindu sense; the text focuses on his role as a vast cosmic being who manifests in countless forms to guide beings toward Buddhahood, not as the creator of the cosmos itself.