It is not clear what you are confused about so I'm going to dissect your post and explain several aspects. It would help if you stated, for example, what is a rest stroke?, or what is imami?, etc.
The post is describing exercises for developing the fingers of the right hand so that they are capable of independently producing different volume and tone when striking notes. There are several techniques to develop for the right hand. Two that come to mind are playing arpeggios on 4 strings while holding a chord and tremolo (playing one note on a single string very fast). There are left hand exercises that do not use the right hand, and right hand exercises that do not use the left hand, each designed to isolate the hand and develop skills without confusion. Once each hand works independently there are exercises that help develop synchronization of the hands, and of course MUSIC.
Some classic examples are "La Technica Degli Arpeggi", and the Giuliani exercises. The first are finger combinations in 4, 6, and 8 notes (at least) on open string followed by some left hand finger patterns while Giuliani provides the same with chord progressions (usually I V7 I over and over).
Right hand fingers (the letter is derived from the Spanish word for each, I think)
i = index
m = middle
a = ring
p = thumb
It is tough enough to get a smooth flow of finger movement but the specific point made in the post is to develop the ability to accent one of the 4 without losing the flow. The capital letter indicates accent (think of playing that one loudly compared to the others).
"Rest stroke" refers to the techniques of letting the finger or thumb come to rest on the next string after striking the string you are playing. This other techniques is free stroke where the fingers do not touch the neighboring strings. This was once heralded as a superior technique for producing a full, rich, tone with volume. The fact is free stroke can be developed to be just as strong with practice and many classical guitarists prefer free to rest. It is really a mater of taste in my opinion. But once you've spent years training yourself it will be hard to retrain yourself, you'll feel like a beginner.
As for the variety of tone produced by flesh, nail, and angle of attack... The "tone" of the note depends on the attack on the string. Much of this is understood from the physics of vibrating strings. Turning the finger just a few degrees before striking or releasing the string can radically change the quality of sound. Many guitarists will create a brighter tone by plucking the strings closer to the bridge. While the physics of this makes sense one sacrifices other qualities. Pepe Romero's book teaches that one should develop variety of tone by adjusting the right hand angle and pressure at the back end of the sound hole (typically the preferred location of the right hand) rather than moving the right hand around.
Pinky sleeps: An interesting description. We almost never use the pinky (at least it doesn't seem to be traditional) but Eliot Fisk (one of Segovia's students) has recommended doing all of Segovia's scales exercises using the pinky to develop better strength and agility in the right hand. It seems that exercising the pinky helps the ring finger.
It seems that the post you've cut and pasted is describing the whole process of 1. working the right hand on one string, 2. working differing pressure and attack, 3. Adding in the left hand. This is done systematically to help develop independent skills and eventually two hand coordination.
I've never heard the specific quote attributed to Segovia. Many young guitarists are happy enough being able to play a chord progression or a few quick runs. But in fact you have 8 independent instruments (1, 2, 3, 4) fingers of the left hand and (p, i, m, a) of the right. It is possible to produce several sounds at once with practice. You can hear that quality in people like Fisk, Parkening, Verdery, etc.