1) Diminished Chord is formed by the Root, Flat 3rd, Flat 5th and Flat 7th.
In general, a 7th is just an addition of the 7th note to the chord. A major 7th is formed by the addition of the 7th note of the major scale corresponding to the root note of the major chord(usually represented by an M7 or triangle). i.e.- CM7- C E G B
A minor 7th is the addition of the 7th note of the minor scale corresponding to the root note of the minor chord (represented by m7).
Cm7- C Eb G Bb
Dominant 7th: These are also referred to as just 7ths. These chords are formed by adding the b7th note of the major scale corresponding to the root note of the major chord (represented by 7).
C7- C E G Bb
9ths are just extensions of 7ths. Add the 9th note of the major (or minor though they're the same note) scale of the root note to the chord and it becomes a 9th.
CM9- C E G B D
It is interesting to note that C E G and G B D make up the C major and G major chord respectively. Thus, playing a G major arpeggion over a C chord should give you a major 9th sound and is quite "pretty".
Cm9- C Eb G Bb D
C9- C E G Bb D
Similarly for 11ths, you add the 11th note to the 9th chord-
CM11- C E G B D F
and so on with 13ths
CM13- C E G B D F A
Since there are so many notes, it's impractical to play all of them at once on the guitar so you tend to skip notes like the 5th, 9th, 11th and sometimes even the root. The 3rd and 7th are the guide tones for the chord (i.e.- telling us whether the chord is major/minor or dom7th) so they should be played.
I'm not sure if this clears anything up. Feel free to ask questions.
And surely you’ll buy your pint cup !
and surely I’ll buy mine !
And we'll take a cup o’ kindness yet,
for auld lang syne.