Short answers, pulled from the story.
Teotl is the central concept in Nahua metaphysics, defined as a single, dynamic, vivifying, eternally self-generating and self-regenerating sacred power, energy or force. It is sometimes translated as god, but it carried more abstract aspects of divinity, closer to the Polynesian concept of Mana. Scholars such as James Maffie and Louise M. Burkhart argue that teotl makes Aztec religion a form of monist pantheism.
The most important deities were Huitzilopochtli, the sun and war god and patron of the Mexica, and Tlaloc, the pan-Mesoamerican god of lightning, rain, water, and thunder. Both had shrines at the top of the Great Temple in Tenochtitlan. Tezcatlipoca and Quetzalcoatl also held central roles, with roots in older Mesoamerican civilizations predating the Aztecs.
The New Fire ceremony, called xiuhmolpilli, was held every 52 years when the ritual and agricultural calendars coincided. Commoners destroyed house utensils and extinguished all fires. Priests marched to the top of the volcano Huixachtlan and waited for the constellation known as the fire drill (Orion's belt) to rise, then sacrificed a man and lit a new fire in his chest cavity. That flame was carried throughout Tenochtitlan to relight all ceremonial fires.
Human sacrifice was understood as a cosmic necessity. According to the myth of the five suns, recorded in the Codex Chimalpopoca, the god Nanahuatzin sacrificed himself to cause the fifth and final sun to rise. Humans were responsible for sustaining that sun's movement through blood offerings. The larger the favor required of a god, the greater the required sacrifice, and blood was believed to feed the gods and prevent the sun from falling.
According to Ross Hassig, between 10,000 and 80,400 people were sacrificed over four days during the dedication of the Great Pyramid in 1487. Archaeological excavations of offerings at the main temple have yielded dozens of remains, far fewer than the thousands recorded in eyewitness and historical accounts.
After the Spanish conquest, Franciscan monks incorporated Aztec song and dance into Christian services, producing a religious syncretism. Aztecs began treating Catholic saints as they had treated patron deities, making pilgrimages to sites often built over old Aztec religious centers. The Virgin of Guadalupe was venerated in ways that closely paralleled worship of major Aztec gods, and the Dia de los Muertos preserves Aztec ideas about the afterlife and ancestors.