Quite. I had other things to do - like playing Mass Effect 3, so please, no spoilers.
You're viewing this stuff as though these "borders" are meaningful.
They are included in the game, ergo they're canon. You criticize me for cherry-picking, but you're doing the same here.
Civilization isn't based on gross distance from a given reference point, e.g. the Citadel, it's based on distance from a mass relay that has been opened and properly charted. A proper map of Citadel space would show little islands around certain mass relays, with smaller islands within easy traditional FTL transit of those mass relays. So the notion of having a very large portion of the galaxy that is very poorly colonized and explored - leaving this proverbial "crack" - yet still regularly transited by Citadel vessels and large-scale trading is completely natural.
Yes and no. (I have the feeling we're essentially speaking about the same thing, but you stubbornly insist on calling things differently, as usual). Primary relays are the galactic superhighways (or high-speed railways if you will) - they can jump ships over thousands, even tens of thousands of light-years. Secondary relays - which are far more numerous - only send ships to relays a few hundred light-years away. To put things in perspective, the "Local Bubble" - an area of space in which our sun currently resides - is only about 300 ly wide. In other words, it would register as a tiny dot on the map.
The Milky Way galaxy is pretty large - 100,000 light-years in diameter. If an average distance between secondary relay was, say, 300 ly, a ship would have to make 333 jumps to travel across it in a straight line (impossible because of the galactic core) and even that assuming there are no "dead ends", i.e. secondary relays which only connect to one other secondary relay.
Therefore, it *does* make sense to speak of a wider galactic frontier - not in terms of distance measured in "conventional FTL flight times", but in terms of space that is easily accessible through mass relays. In practice, it means that civilization spreads to new galactic regions first through primary relays, then through secondary relays, and then through conventional FTL.
In my view, "Earth space" was on/beyond this frontier - too far in secondary mass relay distance (=too many jumps) from the major centres of civilization for anyone to bother really charting it, much less settling it. The Batarians were those willing to do it, but they run into the Systems Alliance in the process. It is also possible that when the humans travelled to Arcturus, they activated the dormant primary relays in that system, effectively connecting what is called "Earth Space" on the map to the rest of the known primary relay "superhighway" network.
What the map shows as "Earth Space" may thus be an area of space that is close to Sol/Earth's major colonies in terms of secondary mass relay distance and is thus its primary area of interest.
(Note: I often hear from people that 2D maps of space make no sense, since space is three-dimensional. That is true, but in case of galactic scale maps, 2D is actually viable. The galactic disc is 100,000 ly in diameter, but it's very thin, just about 500-100 ly.)
As the Codex all the way back in ME1 said, the Terminus isn't really a region of the galaxy with easily defined borders. It's just all the territory outside Citadel jurisdiction - so it encompasses basically all uncolonized and unclaimed worlds, many of which are within the region of space described as "Council space", in addition to worlds controlled by organized polities that claim to be independent from Council control, primarily in the "northern" section of the galaxy spinward from the Citadel and the homeworlds of the Council species. Even within the Apien Crest, home of Palaven and several other early turian colonies (e.g. Digeris), the overwhelming majority of star systems have not been claimed by the Council, let alone explored and colonized; they fall under the term "Terminus", despite being in the heart of what, on the Galaxy at War map, is described as Council space.
Not really. What gives "Terminus Systems" its distinction is that it is a web of systems that are (a) opposed to the Council's authority, (b) closer to each other in secondary mass relay distance than they are to the Citadel space systems. Calling independent worlds inside Citadel space as "members" of Terminus Systems is incorrect.
So describing a whole region of the galaxy as the "fringe" is silly.
No it's not if you understand it in the correct context.
No one region is a "fringe" of explored space. They are all very poorly explored and colonized, especially once one ventures away from the charted mass relay network. Hence my comment about the "cracks" between relays. In reality, these aren't cracks at all, but oceans compared to the tiny atolls of civilized space near mass relays. If you teleported between already-explored atolls and never actually sailed a ship between them, you'd never know that there might be other islands out there in the ocean, too. Same with the relay network.
Again, primary vs. secondary relays. Huge difference.
The "gross oversimplification" refers to the Galaxy at War map, the only one that shows any borders. The in-game galaxy map on which Shepard plots the Normandy's course is not the same thing. It depicts the route, via mass relays (some of which lie in systems the Normandy can't even visit, so we know that this is the actual route, not an oversimplification), that the SR-1/SR-2 takes to get to any given cluster. For all intents and purposes, the depiction of what mass relays the Normandy uses to get to any given destination on the galaxy map can be regarded as canonical.
That is debatable. The map doesn't differentiate between the type of relays SR-1/2 is using when it enters a system. The only one that was identified clearly as a primary relay was the Omega-4 relay.
Also, nice headcanon-map-that-is-directly-contradicted-by-
Mass Effect 3.

Where'd you find it?
I don't remember, probably google search.