Do the edges of the garage door need to be sheathed with a full piece? Of course, the piece would have to be notched out (it will look like an upside down L). I was going to use some scrap pieces, unless it isn't advisable to do so. The garage is a gable style structure with the door cut out of the end.
Yes, try to use as large a piece as possible. With the big hole cut in that end, it doesn't leave much for structural shear. But mainly I would follow the plans. The wall will have been engineered for all stresses involved and you wouldn't have a worry it could blow or fall over. That's where "shear panels" come in, special bolted, special nail pattern, certain minimum width, and extra stud members. Scraps are just that. Be safe, GBAR