1) Using the C Major scale as an example, if you take a look at it you will notice that the scale is comprised of various types of intervals.
C-D-E-F-G-A-B
From C to D is a Major 2nd
From D to E is a Major 2nd
But, From E to F is a half step and therfore a minor 2nd.
Also, From C to E is a Major 3rd
But, from E to G is a minor thrid
An interval is just the distance between any two notes. Therefore, it is the arrangement of intervals that make-up or create the scale and not the other way around.
2) Right. As I mentioned in the answer to your first question, its all about the distance between any two notes and that distance is measured in half and whole steps. So, from C to F is a Perfect 4th becuase the distance between the two notes adds up to a total of 2 Whole steps and 1 Half step. The same is true about E to A. E to A is also a Perfect fourth because if you count up the number of Half and Whole steps from the note E up to A you will see that it also comes to a total of 2 Whole steps and 1 Half step.
3) When a perfect interval is inverted it will still remain perfect. The only thing that changes is whether or not its a 4th or a 5th. For example, From C to F is a Perfect 4th because it has 2 Whole steps and 1 Half step. If we invert the two notes so that we are now going from F to C you will notice that after counting the number of whole and half steps will give you a perfect 5th. 4ths and 5ths (Octaves and Unisons as well) are the only intervals that can be perfect.
4) You can download a free version of Finale Notepad 2007 here:
NotePad