Godzilla being a Planimal kaiju adds a lot of explanation on how Godzilla was able use his Breath Weapon or any other energy-based attacks. Plants have the role of absorbing sunlight or solar radiation and storing it inside to produce food. The evolutionary path taken for the plant may have expanded the trait on absorbing other forms of energy, including nuclear. Plants could also actually in fact produce electricity, which adds more to Godzilla's power.
In relation to the above, Godzilla originating from plants really does make his age, and near-immortality (if he isnt truly immortal), not as far-fetched as it may seem. Apart from the film mentioning lotus seeds surviving some two thousand years, Real Life's oldest known and still-living individual trees are the Great Basin bristle pinecones in California and Nevada, between four to five thousand years old. In addition, there are colonies of Huon Pines and quaking aspen in Tasmania and Utah (respectively) that are estimated to be 10- and 80-thousand years old (again, respectively).
Mecha-Godzilla's role in City on the Edge of Battle is a love letter to all of the previous Mecha-Godzillas' respective roles. He's an alien machine like the first, designed also by humans to counter all of Godzilla's known abilities like the second, and is capable of going "berserk" like the third one did. Just like the original 1974 Mecha-Godzilla, he proves to be a greater threat to humanity than Godzilla ever was, forcing Haruo to work with Godzilla to destroy him. Heck, just like in the 1974 file, Mecha-Godzilla is only defeated when its head is destroyed!
During Haruo's narration, it appears Godzilla was the last kaiju to show up while the other monsters are on a rampage. However if you see a few scenes eariler, Operation Hedorah was successful in defeating both Rodan and Angurirus in a scene which appears to be the former's remains. Why is this Fridge Horror? Remember as early as the Showa saga, Godzilla was Fire-Forged Friends with the both of them, and killing one of them will result in Godzilla avenging them? Now go back to Godzilla's various rampages across the planet: Godzilla is actively seeking revenge, and what's the Central Themeagain?