I've been really busy with school these past 2 weeks, so I wasn't able to get a chapter out... until now!
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The military comment is because Korea has a law that requires every male citizen to serve in the military for 2 years iirc. Often they will take breaks from college to do this, so basically she's wondering if he's already done his time or if he'll have to go away soon.
I think "Kimchi soup" has the same meaning of "Counting the chicken before they hatch" idioms. Sorry if I'm wrong, I only know enough to have a normal conversation.
by does he need to go to the military i think theyre referencing whether he's done his required 2 years. if he's younger, there's a chance he hasn't and she'd have to have a 2 year break waiting for him to come back