Hi Kirk,
It would appear things have gotten a little out of hand here. First I'll help answer your question though!
Order statuses are based on various states on the order, specifically, various fields on the order. You can tell what aspects of the lifecycle an order is in based on a few fields.
Orders that are in the 'paid' state are those that you generally want to fulfill. Other states such as authorized mean that the funds haven't been captured yet.
An order that shouldn't be fulfilled will have it's cancelled_at date set. If the cancelled_at date is null then you know an order should still be processed.
Finally an archived order is just one that has had it's closed_at date set.
From what I understand you are doing CSV exports and using that information to send your fulfillment information off to your fulfillment service. If you want to keep using this route, you'll need to go through those various fields to ensure that an order should be fulfilled before sending off the request.
Depending on what you are using you may want to have a kind of Order object that wraps a CSV row and lets you ask the relevant questions before sending the fulfillment request. Some of those might be something like isCancelled or requiresFulfillment?