Your quilt top is beautiful. To answer your first question, the carpenter's star is often done as one big star (which makes for a relatively fast and easy quilt top) but is also done as multiple smaller stars. One example is on this blog -
http://sunporchquilts.com/. If you decide you do want to finish the quilting, and if not much quilting is already done, you might consider taking out the quilting and then quilting it in sections. There are several methods of how to do this described in Marti Michell's book, Machine Quilting in Sections. I've done that on kingsize quilts and it can be done relatively easily on a home machine. The other option would be to send the top to a longarmer, but I am afraid you or the longarmer would need to take out the stitching already done. Unless the whole quilt sandwich has been well stabilized, the longarmer would have trouble loading a partly quilted item. Taking out quilting is not nearly as bad as it sounds. I have done it...frequently...