“..Mental faculties .. are in truth of the inherent properties of the soul

...Now concerning mental faculties, they are in truth of the inherent properties of the soul, even as the radiation of light is the essential property of the sun. The rays of the sun are renewed but the sun itself is ever the same and unchanged. Consider how the human intellect develops and weakens, and may at times come to naught, whereas the soul changeth not. For the mind to manifest itself, the human body must be whole; and a sound mind cannot be but in a sound body, whereas the soul dependeth not upon the body. It is through the power of the soul that the mind comprehendeth, imagineth and exerteth its influence, whilst the soul is a power that is free. The mind comprehendeth the abstract by the aid of the concrete, but the soul hath limitless manifestations of its own. The mind is circumscribed, the soul limitless. It is by the aid of such senses as those of sight, hearing, taste, smell and touch, that the mind comprehendeth, whereas the soul is free from all agencies. The soul as thou observest, whether it be in sleep or waking, is in motion and ever active. Possibly it may, whilst in a dream, unravel an intricate problem, incapable of solution in the waking state. The mind, moreover, understandeth not whilst the senses have ceased to function, and in the embryonic stage and in early infancy the reasoning power is totally absent, whereas the soul is ever endowed with full strength. In short, the proofs are many that go to show that despite the loss of reason, the power of the soul would still continue to exist. 
(‘Abdu’l-Baha, ‘Tablet to August Forel’)

"That which is born of the flesh is flesh; and that which is born of the Spirit is spirit"(John 3:6) – explanation by ‘Abdu’l-Baha

Christ announced, "That which is born of the flesh is flesh; and that which is born of the Spirit is spirit," meaning that man must be born again. As the babe is born into the light of this physical world, so must the physical and intellectual man be born into the light of the world of Divinity. 
('Abdu'l-Baha, The Promulgation of Universal Peace)

“…physical ailments, no matter how severe, cannot bring any change in the inherent condition of the soul…”

Regarding your questions concerning the condition of the soul during illness. The passages in the "Gleanings" make it quite clear that physical ailments, no matter how severe, cannot bring any change in the inherent condition of the soul, As Baha'u'llah says: 'The spirit is permanent and steadfast in its station'. The veil or hindrance that interposes between soul and body during physical disease is sickness itself. Sickness reveals a lack of balance in human organism, an absence of equilibrium in the forces essential for the normal functioning of the human body. 
(From a letter written on behalf of Shoghi Effendi to an individual believer, March 8, 1936; compilation: ‘Lights of Guidance’)

When the “seed of the spirit” starts to “grow in the human soul”

When a person becomes a Baha'i, actually what takes place is that the seed of the spirit starts to grow in the human soul. This seed must be watered by the outpourings of the Holy Spirit. These gifts of the spirit are received through prayer, meditation, study of the Holy Utterances and service to the Cause of God. The fact of the matter is that service in the Cause is like the plough which ploughs the physical soil when seeds are sown. It is necessary that the soil be ploughed up, so that it can be enriched, and thus cause a stronger growth of the seed. In exactly the same way the evolution of the spirit takes place through ploughing up the soil of the heart so that it is a constant reflection of the Holy Spirit. In this way the human spirit grows and develops by leaps and bounds.

Naturally there will be periods of distress and difficulty, and even severe tests; but if that person turns firmly toward the divine Manifestation, studies carefully His spiritual teachings and receives the blessings of the Holy Spirit, he will find that in reality these tests and difficulties have been the gifts of God to enable him to grow and develop." 
(From a letter written on behalf of the Guardian to an individual believer, October 6, 1954; compilation: Living the Life; compilation: Lights of Guidance)

Spiritual fasting assists the soul “to refresh and reinvigorate the spiritual forces latent” in it

Shoghi Effendi indicates that the fasting period, which involves complete abstention from food and drink from sunrise till sunset, is ‘...essentially a period of meditation and prayer, of spiritual recuperation, during which the believer must strive to make the necessary readjustments in his inner life, and to refresh and reinvigorate the spiritual forces latent in his soul. Its significance and purpose are, therefore, fundamentally spiritual in character. Fasting is symbolic, and a reminder of abstinence from selfish and carnal desires.’ 
(The Universal House of Justice, ‘Notes’ section of the ‘Kitab-i-Aqdas’)

God has “endowed every soul with the capacity to recognize the signs of God”

He[God] hath endowed every soul with the capacity to recognize the signs of God. How could He, otherwise, have fulfilled His testimony unto men, if ye be of them that ponder His Cause in their hearts. He will never deal unjustly with any one, neither will He task a soul beyond its power. He, verily, is the Compassionate, the All-Merciful. 
(Baha'u'llah, Gleanings from the Writings of Baha'u'llah)

The soul’s “progress and success, in all the worlds of God” is dependent on the virtue of ”truthfulness”

Truthfulness is the foundation of all human virtues. Without truthfulness progress and success, in all the worlds of God, are impossible for any soul. When this holy attribute is established in man, all the divine qualities will also be acquired. 
(‘Abdu’l-Baha, quoted by Shoghi Effendi, ‘The Advent of Divine Justice’)