1: Princess is spelled with 2 s's

2:

Once the radiation dies

should use "Once the radiation dissapates".

3:

I can’t watch it forever though I have other thighs to attend to.

should have a comma and "as" before the "I"

4: (From the above) Thighs? Do you mean things?

5:

"Well are you ready, Gemstone.”

should have a comma before "are" and not after "ready"

6: There should also be a question mark at the end of the sentence.

7:

“I Don’t know.”

Don't shouldn't be capitalized.

8:

"Of course we’ve tested it on other ponies. Do you think I would want to go through with this without prior testing"

should also have a question mark.

9:

She has the endurance and strength of her mother Limestone and the confidence of her father Geode.

should have a comma (,) before the second "and".

10:

"All ponies accounted for empress."

Empress should be capitalized.

11:

"Very well you may begin."

should also have a comma before the "you".

12:

The cryogenic sequence was fast to take effect. After the cryogenic seaquants Fully initialized I examined the pods.

seaquants? huh? Did you mean sequence? How did you spell it right the first time?

13: "Fully" (from the above quote) shouldn't be capitalized.

14:

Gemstone Diamond, and Starlight Glimmer were in two of the pods while the rest were irrelevant.

shouldn't have a comma

15:

Starlight may have supported both sides during the war by helping fluttershy develop the megaspells for Mass Healing and then helped the zebras weaponize them, but the desire to make them stronger was something a couldn't let slip away.

Capitalize Fluttershy

16: Either capitalize Megaspells or put a space in between Mega spells.

17: Add a comma before the first "and".

18: "Something a SHE couldn't let slip away"

19, 20, 21, 22, 23:

There was a cryo-container meant for holding DNA samples. I examined the labels on them through the glass. Most of them were irrelevant but two stood out. One had the DNA of a mare named Rainbow Dash, WHILE the other one had the DNA of a stallion named Sorin Soarin'. Those will come in handy (handy? do you mean hoofy?) BE USEFUL. I plan to wait for this Littlepip she blabbered about to die, AND then I'll strike.

This has potential. I've wondered about a Fallout Equestria that has stuff from later series, but you need to be able to tell the story without grammatical errors. I use Grammarly, but you also need a keen eye to spot stuff the A.I. won't see.