The Catian mothership is dangerously large, so much so that if it crashed into the Earth there would be an Extinction Level Event. This is an issue in the series for about one minute, before it's explained that they know this already, and they deliberately designed the ship to break up to prevent that from happening. So only those who are actually on the ship at the time are in any real danger. This way there can still be an epic rescue mission without making the spaceship designers look like reckless idiots.
The Catians' Nudifier weapons are described as "anti-matter". Antimatterdoes not work that way. A weapon firing actual antimatter would release deadly doses of radiation when annihilating anything and be far more deadly than any Earth weapon. The series does not even lampshade this, unlike all the other Acceptable Breaks from Reality they have deliberately made and had fun with under Rule of Cool. That is because they are not antimatter weapons (weapons using antimatter), they are anti-matter weapons (weapons that only affect inert matter, as opposed to anti-personnel weapons that kill people).
The English dub gets around it in another way. In the English dub they are called "quasi-anti-matter" weapons. "Quasi" meaning "seemingly, or almost, but not quite", so they are explicitly not actually anti-matter weapons.
Keeping a Catian from going into heat would be relatively easy for a species that can change their genetics on the fly. It would not be significantly more complicated than modern birth-control methods that prevent periods. The Doylist explanation for why they do not do it is Fanservice. But the Watsonian explanation is exactly the same, just targeted differently. The reason Eris keeps going into heat is because she enjoys it, and trying to mandate that sort of thing from above would be like herding cats.
The Catians' homeworld's name is Earth and its inhabitants are called Earthlings; Catia is the name they adopted in order to avoid confusions with the humans. What else would a race call the land they walk and live on, prior to realizing it's a celestial body?
Justified: The Japanese word for the planet Earth is chikyuu, meaning "earth/ground sphere". A name like this would be pretty universal, no matter the language.
