For the second lesson from Music Theory I, when learning all the major scales in different positions, do we need to find the positions ourselves for each key, and memorize them too? Or is there a systematic way to find them out?
Another thing is, is it helpful to learn all the 12 major scales in one string, or can we just know c major scale in one string as long as we know the intervals between the notes, which will be the same for all the 12 major scales?
In the end it may depend what you're goal is and current level of knowledge. If you're moving from C major to G major and F major then try to understand those things as well as possible. It's more a case of memorization coming from experience and repetition. In the end you just know that G major has one sharp and it's F# and you know where that is all over the guitar. As Tomo says, don't expect too fast.
From a music theory standpoint the major scale has the intervals:
T T S T T T S (T for Tone, S for Semitone)
If you apply Solfege as a moveable Do it's Do Re Mi Fa So La Ti Do - where Do is the root note and you can apply that to aurally work things out. Again, you'll hear that with time.
If you know the above you can apply it to play any major scale anywhere.
You can also look up the circle of fifths if you want a systematic way of working out sharps/flats - although if you know the names of the notes on the guitar your can start on e.g. Bb and work out what the notes are in that major key for yourself