I recently learned the 3-notes-per-string approach for the major scale as it is described here:

But I only learned the first pattern (starting on the root of the major scale).
Now I wanted to figure out the solo of "Blood to Bleed" by "Rise Against".
I know that tabs exist but my intention was to figure it all out by ear.
So the first thing I did was finding the right key of the song.
To make things easier I took a tab of this song, wrote out the notes that are played in this song and used http://www.all-guitar-chords.com/guitar_scales.php to show me a specific scale. E major (Ionian) was the scale which included every note.

First question: Is my approach correct and is it really E major?

So from this point on I closed the tab and figured it out by myself. It sounds pretty cool but I played the whole solo in only one pattern (starting from the 12th fret of the low E-string). Whenever I see a tab with a solo or watch Rise Against playing live I see that they switch positions.

What are the advantages of switching positions if one can play the whole solo in one position?
Is it useful to learn the other positions described in the link above as well?

Now I am trying to figure out "Like the Angel", also by "Rise Against" using the same approach as described above.
I came up with G#/Ab but noticed that some notes are not in the scale.

Is this right or is this song rather written in another key?

Thanks in advance!