I haven't read all of it yet, but it seems to only consider one horizontal of time (as by the theory proposed in this thread).
That's the starting point yes, but if you read on, you will find that this line of time is modified to a sheet of personal lines of time instead. Your 2-D time is possible, I'm sure, but it's much more complicated, and thus less desirable.

And the reason Ellone can't change the past is because she can't alter the present from the past, however, she was able to change a small detail - laguna says that they thought fairies were floating over them to make them stronger, or something of the sort, as a direct effect of Ellone's interference.
The reason she can't change the past is because time is set in stone. At least, that's it as far as I'm concerned. In other words, she couldn't change the past, because things always happened like that. This explains your point of the fairies; those fairies were always there, because all of time exist all at once.

Just read it all through, and then direct any questions here.