Yes. There are many different fingerings for major scales. I was going to write about it on the last post, but I didn't want to write to much or take a chance on confusing you. Since you seem to understand what I was saying, yes the box (sometimes called 3-note per string) has different variations.
The most important to learn are each 5 positions which draws from the start root of each of the 5 different strings (there are 6, but 2 e strings count as one). So if your starting root was on the A string instead of the E, the pattern would be different. Here's the pattern if it's on A.
e|---|---|---|-X-|---|-X-|-R-|
b|---|-X-|---|-X-|-X-|---|-X-|
g|-X-|---|-X-|-R-|---|---|---|
d|-X-|-X-|---|-X-|---|---|---|
a|-x-|-R-|---|-X-|---|---|---|
e|---|-x-|---|-x-|---|---|---|
i m r p last 2 strings it becomes.
i slide i m r p
Work them out for each string, if you don't already have them somewhere. The small x's signify the notes of the scale that exist before the starting root, you don't need to practice them but at least be familiar with them.
The other important one, but doesn't take as much effort, is if the root note is an open string. Here's what that one looks like on open E.
e|---|-X-|---|-X-|---|
b|---|-X-|---|-X-|---|
g|-X-|-X-|---|-X-|---|
d|-X-|-R-|---|-X-|---|
a|---|-X-|---|-X-|---|
e|---|-X-|---|-X-|---|
Then figure that pattern for each of the 5 different strings.
Once your familar with all those patterns: root on each of the 5 different strings, and when the root is an open string. You have a good grip on your major scale, and you should be able to play any major scale sequence anywhere on the neck. Beginners get stuck here because they usually only learn one position or just a few and then find it hard to find the scales at different points on the neck.
Once you get past that, then I'm sure you'll start learning the minor scale, then harmonic and melodic minor, and then whole-tone and other symmetric scales. Doing this for each of these scales will not only improve your scale knowledge but your dexterity at playing in many areas. You can use this as it applies to what your learning out of the book you got.
The stretching version (1-3-5) is not a bad habit, many guitarists use that at certain points in a riff. As for using it when practicing scales, it can become awkward and may cause alittle strain especially on the lower frets. Up higher above the 10th fret or on, it's not so bad. Use the stretching only if you must, as in special purposes.
If your wanting to learn theory, you should learn theory while your learning your scales. So if your learning your major scale, you should read up on the theory behind the major scale. The "wwh" step thing, intervals, and chord that come from each of the tones in the scale. I wouldn't read up on major scale theory while practicing the minor scales, or learn all the scales then try to learn theory all at once. As your learning something, learn theory about it at the same time. Your mind is like a library, if you catalogue all your ideas together, there's less chance of getting confused.
"My whole life is a dark room...ONE BIG DARK ROOM" - a.f.i.