Short answers, pulled from the story.
Mahayana is the largest branch of Buddhism, a broad group of traditions, texts, philosophies and practices that developed in the Amaravati region of ancient India from around the 1st century BCE. It accepts the main teachings of early Buddhism but adds the Mahayana sutras, the bodhisattva path and Prajnaparamita. It is also called the Bodhisattva Vehicle.
Mahayana developed in ancient India from around the 1st century BCE, though its exact origins are debated. Theories place it within the Mahasamghika tradition near the Krishna River in the Andhra region, among forest-dwelling ascetics, or as a textual movement centered on revealing and spreading Mahayana sutras.
Mahayana recognizes doctrines and texts, including the Mahayana sutras, that Theravada does not accept as original, and it sees the bodhisattva path to full buddhahood as superior to the arhat goal. It includes Buddhas and bodhisattvas such as Amitabha and Vairocana not found in Theravada, plus concepts like trikaya and upaya. As of 2010-53% of Buddhists belonged to East Asian Mahayana and 6% to Vajrayana, compared to 36% to Theravada.
A bodhisattva is someone striving to become a fully awakened Buddha for the benefit of all sentient beings. In Mahayana the term applies to anyone from the moment bodhicitta, the wish to become a Buddha to help all beings, arises in their mind, without needing a living Buddha present. Popular bodhisattvas include Avalokiteshvara, Manjushri, Tara and Maitreya.
Mahayana traditions are the predominant forms of Buddhism in China, Korea, Japan, Taiwan, Singapore, Vietnam, the Philippines, Malaysia and Indonesia. Because Vajrayana is a tantric form of Mahayana, it is also dominant in Tibet, Mongolia, Bhutan and other Himalayan regions.
Emptiness, or shunyata, is the Madhyamaka teaching founded by the second-century philosopher Nagarjuna that all phenomena lack svabhava, an inherent unchanging nature. The Heart Sutra states that all phenomena are empty, and Madhyamaka adds that emptiness itself is also empty and should not be clung to.
Non-Mahayanists argued that Mahayana teachings had not been taught by the Buddha but were invented by later figures. Mahayana texts responded that the teachings were revealed later when people were ready, were kept safe by beings such as Nagas, or count as the Buddha's word because they accord with the Dharma. Shantideva argued that any inspired utterance connected with the truth qualifies.