Dragon1
Rear Admiral
To address the original question on the service branches, the US Army and Navy in WWII each operated their own internal Air Forces (one often hears reference to the "Army Air Force", for example). Carrier pilots were almost entirely Navy personnel. It was only after the war that all air operations were combined into an independent Air Force (though the US Navy still flies many fighter planes).
Thus, given the deliberate parallels between Wing Commander and the Pacific War, and the knowledge that carriers were considered "useless" before the Kilrathi War began, we can hypothesize that there was no independent TCSF before the war began, and it was only created afterward. This idea is also supported by the fact that (IIRC) all of the carrier pilots that we see in Action Stations have Navy type ranks (if their ranks are given at all).
This definitely makes the most sense, especially since Blair told Flash that he was receiving his rank in the Flight Branch of the Navy in the Wing Commander 3 Novel.
Also, after WC3, the Space Force receives new uniforms. Blair is considered part of the TCSF reserves in the beginning of WC4, and Wilford refers to the three branches of service on the Midway (navy, marine, and space forces) in the ICIS manual.
So, can we safely assume that the Space Force developed into an independent branch of service that only really came into its own after the war? I think most evidence would support that, although I'm sure LOAF could cite something that contradicts this.