Yeah Synfig is more about constructing the artwork instead of drawing it in the traditional sense. Building each control point one at a time is the best way to take advantage of Synfig’s morphing abilities.
As to your questions, right click on the spline segment you want to extend and choose “Insert Item - Smart”. This will add an extra vector point to the line which is basically the same as “extending” it.
As for joining two splines together, place one endpoint above the other, select the end points of both splines (ctrl-left click, cmd-left click on the mac, and draw a bounding box over the area to select both points), right click on one of them and choosing “Link” in the menu. The two lines will be joined, but you also need to link the bezier handles of each endpoint. To do that, extend each bezier handle so they are visible, select both, right click one of them and choose “Link Opposite”. Then right click on the orange spline point that the bezier handles are connected to and choose “Merge Tangents”. Then the two lines will function as one line.
Sounds a little convoluted but it’s not as confusing to do as it is to explain. Hopefully I made sense. Maybe someone more knowledgeable than me has an easier way of doing it.