Hello!
I think there are a few lines that have been translated wrong. I am not an expert myself so take this with a grain of salt, but here were the main points that stood out to me:
1) But I won't betray you with the promises I've said.
This could be better translated to "This is a verbal promise, but I won't betray it", since the emphasis here is that she (referring to the person in the song) has no written proof of her promise, but she asks someone to believe it anyways.
2) Because of the confidence we made during those ten and a few minutes.
This was a very difficult line for me to translate as well, since the word "象る" can mean to either symbolise something or to build something after something, give something a shape that resembles something else. But the point is that 信用 is not confidence, it is trust.
3) The pain doesn't matter.
割に合わない, as far as I have understood, means that something is not worth doing. For example, "Sometimes it is not worth it to be honest", here you could use 割に合わない, so I think a closer translation would be "The pain is not worth it."
4) I'll invite you, I will bring you who don't know anything.
The point here is that she takes the other person *with her*, so something like "I take you, who doesn’t know anything, with me".
5) I shake it up, I can't go back to that city.
Rather than shake it up, 揺蕩う means to waver or to sway to and fro. And in the original she only mentions "Cannot go back to that town", which could be interpreted as "We cannot go back to that town" or "I cannot go back" as you have written. Since there are clearly two people in the song, I think the "We"-version could sound more accurate.
6) It's a one way ride.
"The trace of footsteps we stepped on is one way" has more elements from the original as it mentions the trace of footsteps.
7) Pluto laughs without any concerns.
"'I don't mind', laughs Pluto" is a better translation. The part before "to" is being said and the part after that tells us who is doing and what.
8) It's not just about the grace of waves.
Here since the word "hiku" has no kanji it is a little more difficult to be absolutely sure what it means, but since the next line talks about a sound, I think this means more something like "Played at the mercy of the waves". "Mani mani" means to be at the mercy of something (waves, the wind, gods...). It does not have anything to do with grace.
9) I just heard the sound of Hameln.
"Now rings the sound of Hamelin." could be more accurate, since there is no mention that the characters in the song hear the sound (even thought it is likely the case). But it is more along with the original meaning.
10) I'm smart I know how to take things in with my hands.
手にとるようにわかるのさ is a frase that means to understand something very clearly (almost as if it was actually in your hands). So "The clever me understands this so well" could be better.
11) Because immediately with a self-satisfied look, you can be praised wrongly.
This does not really follow from the original, where there are two separate sentences and it is up to the listener to decide wheter they connect or not (I guess...). So I think "Improvise with a self-satisfied look Because of that wicked praise" could be better. "Yokanaru" means evil or wicked and "Shoushan" means praise.
12) Staring won't heal.
睨む is a very nasty type of staring, so glaring could be better so that feeling comes through in the translation. "Even if I am glared at, it won’t get better".
13) Why do you hang on to Uranus.
The people in the song don't hang on to Uranus, I understood this as "“Why” entreats the Uranus". As in the Uranus is watching them and desperately asking "Why?".
14) Before the grace of night comes.
This has nothing to do with the original one really, this one would be translated more like the previous similar line, "Played at the mercy of the night".
15) I heard a sound.
Here it is important to notice the "から", which as you propably know, means "because". So the point is that the last line of the song is a slightly different version from the "今ハーメルンの音がしたんだ", but instead this time it is "音がしたから" so "Because of that sound..." or "Because that sound rang..." and the sentence is cut there without an ending.

I hope you don't take this in a bad way, this is a very difficult song to translate and there is a lot of Reol-like frasing and imaginery going on and many difficult words. As I said, I am not an expert either, but I hope that these prove useful to you and other people as well.
This is a lovely song, one of the best from this album!