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I am by no means an expert on the subject, so please take my answers with a pinch of salt (that is to say, take my answers with some amount of skepticism, as I may be mistaken). For reference, I speak American English. Also, if I am explaining things which you already know, I apologize. I am not trying to imply you are stupid or do not know something simple; I want to make sure I am being as thorough and complete as possible.

The phrase "mission critical" is used in military jargon as shorthand to mean "critical to the mission." If I said "The safety of the general is mission critical," what I mean is "The safety of the general is critical to the mission." 

"Non-" is a prefix which means "not" or the negation of the word that follows it. For example, the word "Non-negotiable" means "Not negotiable".

So, the author is applying the prefix "Non-" to the phrase "Mission Critical" to create the phrase "Non-mission critical" (which means "not mission critical") This may not be strictly correct (you will not find the phrase "Non-mission critical" in an English dictionary). But, the use of this phrase works in the story because the story is written in first person, using the character's voice to narrate the story, so some intentional grammar mistakes can be made to convey the character's voice, as most people do not speak with perfect grammar. But, the writer needs to be careful that they are not making the text confusing or difficult to read.

In this story, the main character/narrator is a soldier, so the use of jargon like "mission critical" or "non-mission critical" works in the story because it makes the narrator sound like a soldier and it is still understandable as long as the reader is familiar with the jargon being used or is able to intuit the meaning. In this case, it sounds like you were able to intuit the phrase as meaning "not critical for the mission," so it seems to have worked.

Regarding the use of "as", I am afraid I do not have much information to give. In common usage of English (and, I think, most other languages), some words are removed or "dropped" to save time and space when writing or speaking. For example, I started this paragraph with "I am afraid I do not have much information to give" instead of "I am afraid that I do not have much information to give." Including "that" in the sentence does not change the meaning, add any information, or make the sentence easier to read, so I did not bother including it. 

When a word can be "dropped" depends on the sentence, so I cannot give a complete list of examples or circumstances. But, in American English, "as" often is not included after "considered". For example: "Dogs are considered man's best friend," or "This sentence is considered grammatically correct English."

I apologize for the long reply and I hope this is helpful to you!