Extensions are simply scale degrees if you keep counting past an octave. If the scale degree of an octave is 8, the next tone will naturally be a nine. Nines are simply an octave above a two. They appear in notation for "extended" chords, when the tone extends beyond the first 7 tones. Elevens are an octave above a four. Thirteens are an octave above a six. Like many other things in jazz, strict definitions are not adhered to and these tones are loosely interchangeable. You would never call a vi chord a "13 chord," however.
The strings are stacked in fourths, with an offset at the B string to accommodate better fingering. Without accounting for the offset, a 3 generally sits above a 6, a 6 sits above the 2, the 2 sits above the 5, and the 5 sits above the 1. Finally, the 1 sits above the 4. This accounts for all degrees except for the 7, which is naturally a semi-tone down from the root, and somewhat under the 5. Things change when you go from the G to B string, so be aware of this.
It's something you have to learn pretty rote anyways. It's just as handy to understand the intervals going up from the first string as down from the low E string. To quiz yourself, pick a root anywhere on the fretboard. Then look to a string north, south, east or west of it. Guess what the interval is. Now make sure you know both the note names. Check your answer by figuring out if the note name is the same scale degree as you said it was.
For example, put your finger on the 8ths fret of the G string -- this is the root. Now go up to the fourth note of the G string. If you guessed that is the flat 9 or flattened-second scale degree, you are correct. You can double-check with the notes. The first note was a G. The last note was an Ab. A is the the second scale degree of G. The 2 is equivalent to the 9. It's a semi-tone down from the A, so it's a flat 9 or a flat 2.
Here is an online quiz you can do, but it only tests intervals going one way:
Online Interval Quiz