That diagram does not depict the entire universe. At most, it depicts the history of what is now our observable universe (specifically, a 2D slice through it), with us at the center only because we're observing it. Someone at the furthest reaches of that portion of the universe would see us at the furthest reaches of their observable universe, and themselves ...
This is a difficult question to answer. Physics really starts after the big bang. Scientist don't know about the laws, if any, before the first instance after the big bang. The time before and during the big bang is really the province of philosophy.
The big bang (a singularity 13.8 billion years ago that was the beginning of time) didn't happen at all. Inflationary cosmology consists of:
ΛCDM (aka "big bang") cosmology starting at a cosmological time of some small fraction of a second, preceded by
an inflationary epoch lasting for an unknown amount of time (but at least 50-60 e-folds), ...
One flaw is saying that the big bang occurred at a location. It didn't: the whole universe was once part of the big bang. So the stuff about deceleration being seen as acceleration isn't true.
Secondly, shortly after the big bang, the universe behaves "ballistically" (although following the rules of General Relativity, not Newtonian gravity). It was ...
the expansion of the universe is relative to where it is being observed from. Much like dots on a balloon. Its easy to point to the center of the balloon (like what the picture shows) because it is only a 3d object. But for higher dimensions we don't have the spacial awareness to understand where than center of the universe is (if there even is one)
There are theories which suggest that the universe is like a giant spring, constantly expanding and collapsing. Its possible that pre-big-bang, there was another universe which collapsed, only to re-expand into the universe we know now.
But in reality we have no idea