I have a really nice view where my little house will be set and would like to take fullest advantage of it.

Thought I'd approximate a "wall of glass" using sliding glass door units on either the 12x18 or 14x24 on a non-gable side.  This side would face the view and also luckily faces south, so some passive solar heating will result.  I thought I'd have two or three SGD units, seperated by very short walls (possible one wall of 4 to 6 feet for placement of a woodstove).

So my question is using a double header with trimmer and king stud for each door do I need a minimum length of common studing for support?

From a racking resistance point of view you should have a sheathed wall at least 2'-8" wide on each side of the corner. Tie the sheathing into the header (notch out a full sheet) and nail the whole thing off rigid.