I want to put the same web parts in the same order to many courses.
You can copy homepage via ShrePoint Designer from one course to another and set it as a homepage, see screenshot (homepages are under Site Pages section).
The constraint is that default LMS web parts (the ones that were present right after site creation) except "Learners" web part will not be shown on another course. Only web-parts that were added manually will be kept and shown on another course.
Hence there is an easy workaround - you have to manually add needed web parts to the source homepage and copy it to the destination courses.