Why does Marge Simpson have huge blue hair? Why does Godzilla have those dorsal fins? Why is Goofy a human-sized talking dog? It's just how the characters were drawn/created. A lot of characters are given a distinctive look so that the audience can easily recognize him. Maybe Schwarzwald is hiding something under his bandages. Maybe he has a weird deformity. Or, maybe it's just how he looks.
In the finale, how did Dorothy get functional again?
Possibly, the “Memories” that were stolen from her (the disc drive assembly behind her hair ribbon) weren't actually the entirety of her memories and mind, but simply the special legacy ones from pre-wipe. Alternately, various support processors gradually absorbed her thoughts over time, and when the assembly was pulled from her head they managed to pick up the slack, sort of like if somebody's spinal column and central nervous system took over from their brain.
The megadei and androids work partly off of radio signals. In the first season, Dorothy's big sister makes Dorothy copy movements because Dorothy's body can't tell whether the signals come from Dorothy or her big sister. In the finale, the megadeus with Dorothy's 'brain' broadcasts enough of her memories that Dorothy's body regains her self.
It could have easily have been something else. It's just tomatoes were used in the example. Which is due to the fact that synthetic tomatoes have largely if not completely replace real ones at this point.
It's a classic Science Fiction reference for false humanity.
Is it just me, or does it feel like the writers couldn't come up with a perfectly plausible ending and decided to throw the ending together?
The ending was supposed to be complete and wrap things up. Then the writers were told that they might get a third season, and were instructed to make things ambiguous, and leave more questions to be answered in said third season. And thenthey didn't get picked up for a third season.
This explanation rings hollow to a degree, since even now the first season finale also makes precious little sense to me.
The first "finale" is the result of the original 26 episode order getting Cut Short to 13 episodes. So what you have is one half of a whole show that ended at a point where there was no intended resolution (Act1-13), and a second half with an intended resolution altered to support a third season that never happened.
What happened to “R.D.” (Dorothy's Evil Twin)? Who was she? What was she doing?
R.D. got destroyed when Big O smashed her into the ceiling. She was an android that was supposed to kill people with Memories (if that was her original purpose or someone else programmed her to do that, I don't know). I don't remember who activated her or why they did, maybe another troper can answer that.
Why is it the megadeus introduced in Schwarzwald's first appearance was fast and agile when it's established that megadei are Mighty Glaciers?
When is that ever established? Big O is a Mighty Glacier, that doesn't mean they all are. You might as well ask why Big Duo can fly, why Glinda could do gymnastics, and why Constanze could wave its arms around rapidly.
Big Duo had big-ass engines to pull his weight, so that makes sense. And the arms? Less pressure exerted on the arms= moar speed. But the prototype megadeus in the underground room is ninja-like when, obviously, it's a Big-Class robot itself. And all of the other robots walked slowly too. And which one was Glinda?
Glinda is Megadeus that does gymnastics, duh. It was female looking and had a telescoping sword.
The warehouse megadeus is implied to be the base model, minus any customization. No bulky armor or weapons to weigh it down.
To elaborate, the Archetype is a Big-Class Megadeus, designed to carry the ludicrously heavy armor and weapons of the O, Duo, and Fau subtypes, but without any of that. Think of it as taking the engine from a semi and putting it in a go-kart. One other point though. It's really more of a minor quibble. The archetype wasn't lacking customization because there was no customization of the Bigs. The Archetype was a chassis that the bodies of the other Bigs would be attached to. Prior to the Event(s), the Bigs were mass-produced war machines similar to mobile suits from Gundam though... much bigger and slower.
Is there any reason Adult Swim never aires the show from the beginning, but from mid-to-end of the second season?
Adult Swim only has rights to the second season, since they had a hand in producing it, if I recall.