Hi Bastien,
a) The hover box disappear as soon as your mouse quit the blue line, which makes it more of an informational box than a go-to box
Yes, in a sense; it is sometimes possible to keep it open and move your mouse pointer over it, but that isn’t really the intent – it exists really as a box that displays some extra information when you mouse over the event entry itself (and that should also answer your second point/question).
You can see the same thing on our demo site by way of reference.
Does that help?