Ok, you asked for grammatical critiquing, so here it is.
Quotes and the stating of who said them should be separated by commas, not periods. This set:
"Order the Potemkin to fall back. Ravager and Osired are to escort her
." Admiral Roeding ordered, clutching at the railing before him.
Should instead be:
"Order the Potemkin to fall back. Ravager and Osired are to escort her
," Admiral Roeding ordered, clutching at the railing before him.
You've repeated this everywhere. Only when there is a question or exclamation do you use that instead of a comma.
Also, it is generally better to say who said it in the first sentence, rather than the second. This point isn't quite necessary if I remember correctly, so don't worry too much about it. As long as it is fairly close to the beginning of the paragraph it should be fine.