Re: No H or He?
"...at what speed was the border between space and non-space moving?"
There is no "border" between space and non-space, just as there is no "edge" of the Earth. This is the kind of weird shit where you have to try to get your head around higher dimensional spaces, so I'll try to explain in visual terms.
Imagine that you are a 2-dimensional being, like those in Edwin Abbott's Flatland. To you, there is no such thing as "up" and "down"; these concepts simply don't exist in your worldview. Your entire universe consists only of "north-south" and "east-west."
If your 2D universe is mapped onto the surface of a sphere or torus, it would eventually wrap around on itself. If you walked far enough in what seemed to you in all measurable ways to be a straight line, you would eventually return to your original position from the opposite direction in which you set out. It wouldn't matter which direction you chose - north, south, east or west - you would infallibly return from the other direction without ever apparently having changed direction - and without ever encountering any kind of border, edge or boundary.
At the time of the Big Bang in your 2D universe, the sphere or torus would be very small, and you would walk around it and return to your origin in a very short time. But then suddenly the sphere expanded hugely, and that five-minute walk suddenly became a multi-billion-year light-speed hike. But there was no edge or border you could encounter when the universe was small, just as there is no edge or border to be found when it got large.
But, you argue, the sphere does have a border - the limit of its surface. If you move along its radius, instead of its circumference, you've crossed an edge.
Yes, you have. But to do that you had to travel in a direction that, for the 2D inhabitants of the surface of the sphere, simply does not exist except in certain abstract equations. No 2D denizen can ever point in that direction and say "we could go that way!" - because the only possible ways they can see to point to all lie along the circumference of the sphere. How do you explain what "up" and "down" are to beings that cannot understand or perceive those "directions?"
Now expand this thinking into three-dimensional space - our universe. No matter what direction you fly in - north, south, east, west, up or down - if you keep going in a straight line, you will eventually return to where you started, from the opposite direction, without ever encountering any edge or border, no matter where you go or how hard you look. If there is a boundary or edge to space, it is in a higher dimension that we cannot point to or travel in. I could say to you, "you could go "hyperin" or "hyperout" - but what would those words mean to you? How do I point hyperin the way I can point north, east, or up, to direct you hyperout of the universe? Do the words hyperin and hyperout even make sense to you?
At the time of the Big Bang, the universe was very small, so if you walked for five minutes in a straight line you end up back where you started. But then suddenly space expanded hugely, and that five-minute walk suddenly became a multi-billion-year light-speed hike. But there was no edge or border you could encounter when the universe was small, just as there is no edge or border to be found when got large.
Hopefully that imagery will reveal to you the flaw in your question. :)