[REQ] Fate/hollow ataraxia - hollow by Number201 feat rhu

This is a pretty good translation for a beginner! I've got a few notes, but I can see that you've made a solid effort to make things flow.

The blue moon is reflected inside the mirror
-青い月 should be "pale moon." 青い primarily means "blue," but in contexts like this "pale" is better.
-Looks like you left out a translation of 裏側

Overlooking the city full of people that never wakes
-Speaking of 裏側, I took it to mean that the city full of people was the reverse side of the mirror, but frankly it's a difficult image. Not sure of the best way to render these two lines together.

I clawed my fingers towards the weary face reflected in my eyes
-Be careful with multi-kanji verbs like "見飽きた". It's not a weary face, it's a face that someone is tired of looking at.

Sighing as I threw the sealed memories away
-途切れる is interrupted or cut off, not sealed.

Crimes and punishment that repeated
Thrusting and stabbing in my chest

-This one's a matter of taste, but something like "Repeated crimes and punishments" might make it more clear that the crimes and punishment are repeating, not the thrusting and stabbing.

An image of glass crumbling; An array of dreams
-崩れた is past tense, so "broken glass" would be more accurate. Of course, the most literal would be "an image of crumbled glass" which sounds dumb in English.
-I don't think "an array of dreams gives the right image for "ひろい集める夢". "ひろい集める" means to collect or gather. I see where you're coming from, but I think the word choice could be better. "Dreams gathered together"?

Even your name is lost in my memory
-Verbs ending in "そう" indicate that the action could happen, not that it has happened. I'd go with something like "It feels like I might even lose your name"

The flowers on the window scatter, oblivious of their fates
-窓辺 is more literally "by the window"
-I took the "忘れ" here as imperative, but I'm not 100% on that.
-If I'm right, it would make it more like "The flowers by the window scatter; Forget destiny"

Dry memories of being soaked by the merciless rain
-That's an interesting take - due to the space between the two phrases (乾いた記憶　無慈悲な雨に浸した), I took this as "A dried-out memory Soaked by merciless rain". I think your take is a valid reading tho. Either way, you get the dichotomy of dry and soaked.

With your hands, I desperately wished
To stab the heart within my chest
-"切り裂く" is more tearing or cutting apart than stabbing.
-The て in "切り裂いて" combined with "願わくば" made me think this is a request of another person, not something done to oneself. I would go with "I pray that this heart / Will be torn apart by your hands" or "I pray that by your hands / This heart will be torn up."

An image of glass shatters; A torrent of dreams
-探して走る means to run searching after (探して- search, 走る - run). That doesn't translate directly very poetically, so I might go with something like "A dream chased after" or "A dream of chasing after."

Your name alone, I don't want to lose
-This is why the "そう" in the earlier line "君の名前さえも失くしてしまいそう" is so important. We go from feeling like "your name" might be lost/feels like it will be lost to "wanting not to lose the name."
-It looks like you forgot the "から" which changes the meaning of this line to something more like "Because your name is the only thing I don’t want to lose."

Invisible world; Hollow cradle

-透き通る has a meaning closer to transparent than invisible. I think "invisible" could work as a poetic choice, but "transparent world" (a world that you can see through) is a very different image from "invisible world" (a world that you can't see). A matter of taste, I suppose.

Again, I want to emphasize that your translation was very solid for a beginner. I think with a few tweaks, you'll have something to be proud of.