Our go-to example for driving these displays is the Alpha Clock Five. There is example Arduino code there which you may be able to use as a basis for other projects. You can also look at the hardware documentation to see how we drive the different length segments and decimal point.
Adafruit likely has example code for the various components that you linked to– their learning system has lots of resources.
As an open source hardware project, you can learn from it and borrow code from it without purchasing it.
Regarding the number of segments, the 17th segment is actually the decimal point, which means ours technically have 18 with dual decimal points. 17 segment is the usual name used for this kind of display.