In the course i am updating/ renewing, i keep running into
a problem. Some existing verts have many rays coming out of them.
Some verts cannot be deleted. This causes problems in seam-blending
or creating a shape. adding verts etc. Can anything be done?
You'll get plenty of help with this, but let me start. The "rays" are "edges", and appear as straight lines. The verts you mentioned can probably be deleted, but it will require some manipulation. These Lez Marwick Lessons will provide some valuable information, and he explains it well.