No, Mothra is not Godzilla's mother in the main movie continuities. Their relationship is typically one of an ancient ally, symbiotic partner, or powerful queen to his king.
Mothra (モスラ, Mosura), also called The Goddess of Peace, is a giant, divine, butterfly/moth-like deity kaiju goddess, the series quadtagonist, and the Guardian of the Earth. She is Godzilla's closest friend.
Their species have a symbiotic relationship, and they as individuals have a history as allies together. Mothra is essentially Godzilla's sister in arms.
Also, Mothra is given a short origin story in the Heisei series, with the Cosmos explaining that Mothra is a genetically engineered creation of the Cosmos made from fusing the remaining life energy of their race with a common lepidoptera. Mothra is one of the most powerful psychics in the Toho universe.
Battra is a current member of the Earth Conquerors and is The Guadrian of Terra. He is the descendant of the Kaiju of Earth Gigamoth of the Eight Guardians of Terra, the brother of Mothra The Guardian of Mortals and uncle of Mothra Lea and Mothra Leo.
Godzilla movies feature surprisingly emotional deaths, from the tragic fall of Mothra to the selfless sacrifice of Dr. Serizawa. The original 1954 Godzilla's demise is a mixture of relief and tragedy, showcasing the creature as a victim of nuclear testing.
King Ghidorah, and even more so in GMK: Giant Monsters All-out Attack. Even in those two movies, Ghidorah was still a formidable opponent, and the other films have sealed Ghidorah's place in history as Godzilla's greatest foe.
In the new movie however, Godzilla is injured when caught up in Operation Crossroads, an American weapons test. This gives him his atomic breath and also makes him angry towards humans. He now attacks American and Japanese ships, heading towards the Japanese Archipelago.
Anguirus was reintroduced in Destroy All Monsters as an ally and best friend of Godzilla living with him on Monsterland, a role that Anguirus maintained throughout Godzilla vs. Gigan (1972), Godzilla vs. Megalon (1973), and Godzilla vs. Mechagodzilla (1974).
Godzilla has a deep hatred for King Ghidorah, specifically because King Ghidorah caused immense chaos and destruction on Earth.
Godzilla and Mothra Are Married! No Joke - IMDb. As the saying goes, every king needs his queen.
Mothra uses sound as a method of communication more so than the other Titans in the film. He thinks Mothra's stinger could be an ovipositor that she uses to lay her eggs, and jokingly suggested Rodan could be pregnant with her after she impaled him with it during the film.
Shōwa era (1967–1969)
In his debut film, Son of Godzilla, Minilla was born on Sollgel Island, when his egg was prematurely cracked open by a group of mutant giant mantises called Kamacuras.
Regenerative Durability. In the movie, Godzilla's regenerative ability proved to be very potent that any pieces of his flesh that broke off his body grew into starfish-like creatures. This enables him to reproduce asexually through either fission or even self-mutilation.
Mothra is a major character in Monster Island Buddies. She is a Divine Moth kaiju and is married to Rodan. The love triangle between her, Rodan, and King Ghidorah, as well as her relationship with Ghidorah as a whole set off the show's story.
The ending of Godzilla Minus One means that Noriko has radiation poisoning. Whether or not she survives is unknown. During Godzilla Fest in Osaka, director Takashi Yamazaki confirmed that the black marks on Noriko's neck were Godzilla cells or "G-cells".
Enraged, Godzilla prepares to destroy all the vessels with its heat ray, but Shikishima crashes the plane into Godzilla's mouth and destroys its head, causing the energy of the heat ray to tear its body apart.
Godzilla's species, Titanus Gojira, evolved millions of years ago during the Permian period. Though powerful and numerous, they were slowly decimated by the JinshinMushis, a species of parasitic Titans that prey almost exclusively on them.
Following Ghidorah's apparent demise, the skull of his leftover severed head was converted by Apex Cybernetics into a semi-organic psionic control system for Mechagodzilla.
However, he's only actually died in four of them. True to his title, Godzilla typically prevails in most of his fights - even when he's the main villain. Kaiju as powerful as King Ghidorah, Biollante, and Gigan have all failed to bring him down, but not for a lack of trying.
All Monsters Attack (1969)
Although helmed by visionary filmmaker Ishiro Honda, who directed many of the best Godzilla films, “All Monsters Attack” is widely regarded as the worst of the worst, and for good reason.
The original "Godzilla" is far from a lighthearted monster flick; it is a dark and intense film with strong allegorical ties to the atomic bombings of Hiroshima and Nagasaki, and the horrors of nuclear warfare.