You need to twirl open the shape layer groups and select the paths to gain access to the anchor points and move them around with teh standard move/ select tool. Unfortunately AE is pretty dumb and clunky in this area and has no dedicated tools that would make things easier.
about selecting a path
you should allow show layer controls to see the path
now if you click twice on the shape layer you get access to the shape group properties, click another time either on the path or the vertices and you will get access to the path itself.
about the line coming in front and back of the earth
you could do that with a bit of 2D trickery: animate your lines as usual (choose different layer for each stroke so this will be more manageable) and put them below the earth layer. as the line finishes it's course below the earth and appears on top - Duplicate the layer and put in on top of earth and adjust the length and key-frames so it would seem to continue without interruption
you are welcome - please tag the suggestion you were given so others will find it too. thank you