We have [God has] commanded you to pray and fast from the beginning of maturity; this is ordained by God, your Lord and the Lord of your forefathers. He hath exempted from this those who are weak from illness or age, as a bounty from His Presence, and He is the Forgiving, the Generous.
(Baha’u’llah: The Kitab-i-Aqdas, pp. 22-23)

In truth, I say that obligatory prayer and fasting occupy an exalted station in the sight of God.
(Baha’u’llah: Aqdas: Questions and Answers, p. 134)

As regards fasting, it constitutes, together with the obligatory prayers, the two pillars that sustain the revealed Law of God.
(Shoghi Effendi: Directives of the Guardian, p. 27)

For this material fast is an outer token of the spiritual fast; it is a symbol of self-restraint, the withholding of oneself from all appetites of the self, taking on the characteristics of the spirit, being carried away by the breathings of heaven and catching fire from the love of God.
(`Abdu’l-Baha: Selections … `Abdu’l-Baha, p. 70)

Besides all this, prayer and fasting is the cause of awakening and mindfulness and conducive to protection and preservation from tests….
(`Abdu’l-Baha: Baha’i World Faith, p. 368)

The Divine wisdom in fasting is manifold. Among them is this: As during those days (i.e., the period of fasting which the followers afterward observe) the Manifestation of the Sun of Reality, through Divine inspiration, is engaged in the descent (revealing) of Verses, the instituting of Divine Law and the arrangement of teachings, through excessive occupation and intensive attraction there remains no condition or time for eating and drinking. For example, when His Holiness Moses went to Mount Tur (Sinai) and there engaged in instituting the Law of God, He fasted forty days. For the purpose of awakening and admonishing the people of Israel, fasting was enjoined upon them.
Likewise, His Holiness Christ, in the beginning of instituting the Spiritual Law, the systematizing of the teachings and the arrangement of counsels, for forty days abstained from eating and drinking. In the beginning the disciples and Christians fasted. Later the assemblages of the chief Christians changed fasting into lenten observances.
Likewise the Koran having descended in the month of Ramazan, fasting during that month became a duty.
In like manner His Holiness the Supreme (the Bab), in the beginning of the Manifestation through the excessive effect of descending verses, passed days in which His nourishment was reduced to tea only.
Likewise, the Blessed Beauty (Baha’o’llah), when busy with instituting the Divine Teachings and during the days when the Verses (The Word of God) descended continuously, through the great effect of the Verses and the throbbing of the heart, took no food except the least amount.
The purpose is this: In order to follow the Divine Manifestations and for the purpose of admonition and the commemoration of their state, it became incumbent upon the people to fast during those days. For every sincere soul who has a beloved longs to experience that state in which his beloved is. If his beloved is in a state of sorrow, he desires sorrow; if in a state of joy, he desires joy; if in a state of rest, he desires rest; if in a state of trouble, he desires trouble.
Now, since in this Millennial Day, His Holiness the Supreme (the Bab) fasted many days, and the Blessed Beauty (Baha’o’llah) took but little food or drink, it becomes necessary that the friends should follow that example….
(`Abdu’l-Baha: Lights of Guidance, p. 235)

The fasting period, which lasts nineteen days starting as a rule from the second of March every year and ending on the twentieth of the same month, involves complete abstention from food and drink from sunrise till sunset. It 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.
(Shoghi Effendi: Directives of the Guardian, pp. 28-29)

Regarding the nineteen-day fast: Its observance has been enjoined by Baha’u’llah upon all the believers, once they attain the age of fifteen and until they reach seventy. Children of all countries, nationalities and classes who are fifteen years old are under this obligation. It matters not whether they mature later in one country than in another. The command of Baha’u’llah is universal, irrespective of any variance in the age of maturity in different countries and among different peoples.
In the `Aqdas’ Baha’u’llah permits certain exceptions to this general obligation of fasting, among them are included those who do hard work, such as workers in heavy industries.
But while a universal obligation, the observance of the nineteen day fast has been made by Baha’u’llah the sole responsibility of the individual believer.
(Shoghi Effendi: Lights of Guidance, p. 234)

Regarding your question concerning the Fast: Travellers are exempt from fasting, but if they want to fast while they are travelling, they are free to do so. You are exempt the whole period of your travel, not just the hours you are in a train or car, etc. If one eats unconsciously during the fasting hours, this is not breaking the Fast as it is an accident. The age limit is 70 years, but if one desires to fast after the age limit is passed, and is strong enough to, one is free to do so. If during the Fast period a person falls ill and is unable to fast, but recovers before the Fast period is over, he can start to fast again and continue until the end. Of course the Fast, as you know, can only be kept during the month set aside for that purpose.
(Shoghi Effendi: Directives of the Guardian, p. 29)

As to your question regarding the Fast: If there is any doubt in the mind of a person as to whether it will really be bad for that person’s health to keep it, the best doctor’s advice should be obtained. But generally speaking most people can keep it, anywhere in the world, with no detriment to their health. It is very good for the health and, once one forms the habit, each year it becomes easier to keep, unless one is rundown. No one is obliged to keep it if it really harms them.
(Shoghi Effendi: Lights of Guidance, pp. 234-235)