The side is irrelevant, as all virtual reality/pocket dimension.
The speed itself isn't relevant, it's the fact they actually physically move from one place to the next, that's linear time.
1)She does fear EA, she locked Gilgamesh away because she was scared of him.
2) It is relevant in that the character needs that setting to use this skills, a strong character will just escape the mooncell and nuke the moon, like Arcueid did by playing around.
3) I mean Rin explains something that sounds neat but BB showed no practical use for it, the only thing she did was send info to her past self.
4) Well her fighting speed is whatever the other servants that fought her where +, while her hax is instant if she does react to the opponents.