Verily, it is enjoined upon you to offer a feast, once in every month, though only water be served; for God hath purposed to bind hearts together, albeit through both earthly and heavenly means.
(Baha’u’llah: The Kitab-i-Aqdas, p. 40)

This festivity, which is held on a day of the nineteen-day month, was established by His Holiness the Bab, and the Blessed Beauty directed, confirmed and warmly encouraged the holding of it. It is, therefore, of the utmost importance. You should unquestionably see to it with the greatest care, and make its value known, so that it may become solidly established on a permanent basis. Let the beloved of God gather together and associate most lovingly and spiritually and happily with one another, conducting themselves with the greatest courtesy and self-restraint. Let them read the holy verses, as well as essays which are of benefit, and the letters of Abdu’l-Baha; encourage and inspire one another to love each and all; chant the prayers with serenity and joy; give eloquent talks, and praise the matchless Lord.
(`Abdu’l-Baha: The Nineteen Day Feast, p. 425)

As to the Nineteen Day Feast, it rejoiceth mind and heart. If this feast be held in the proper fashion, the friends will, once in nineteen days, find themselves spiritually restored, and endued with a power that is not of this world.
(`Abdu’l-Baha: Selections … `Abdu’l-Baha, p. 91)

In every cycle and dispensation, the feast hath been favoured and loved, and the spreading of a table for the lovers of God hath been considered a praiseworthy act. This is especially the case today, in this dispensation beyond compare, this most generous of ages, when it is highly acclaimed, for it is truly accounted among such gatherings as are held to worship and glorify God. Here the holy verses, the heavenly odes and laudations are intoned, and the heart is quickened, and carried away from itself.
The primary intent is to kindle these stirrings of the spirit, but at the same time it follows quite naturally that those present should partake of food, so that the world of the body may mirror the spirit’s world, and flesh take on the qualities of soul; and just as the spiritual delights are here in profusion, so too the material delights.
Happy are ye, to be observing this rule, with all its mystic meanings, thus keeping the friends of God alert and heedful, and bringing them peace of mind, and joy.
(`Abdu’l-Baha: Selections … `Abdu’l-Baha, pp. 90-91)

The significance of the Nineteen Day Feast is thus threefold. It is a gathering of a devotional, social and administrative importance. When these three features are all combined, this Feast can and will surely yield the best and the maximum of results.
(Shoghi Effendi: Nineteen Day Feast, p. 434)

Also regarding the Nineteen Day Feasts: these are not strictly obligatory, but the believers should endeavour to regularly attend them, mainly for the following two reasons: first, because they foster the spirit of service and fellowship in the community and secondly, in view of the fact that they afford the believers a splendid opportunity to fully discuss the affairs of the Cause and to find ways and means for continued improvement in the conduct of Baha’i activities.
(Shoghi Effendi: Nineteen Day Feast, pp. 439-440)

As to your question concerning Baha’i Feasts, Shoghi Effendi strongly feels that on such occasions the friends should emphasize both the spiritual and the administrative elements. For these are equally essential to the success of every Baha’i festival. To maintain the right balance between them is, therefore, the duty and responsibility of every individual Baha’i or group.
(Shoghi Effendi: Nineteen Day Feast, p. 433)

The main purpose of the Nineteen Day Feasts is to enable individual believers to offer any suggestion to the Local Assembly, which in its turn will pass it to the National Spiritual Assembly.
(Shoghi Effendi: Nineteen Day Feast, p. 451)

In the Arabic Bayan the Bab called upon His followers to gather together once every nineteen days to show hospitality and fellowship. Baha’u’llah here confirms this and notes the unifying role of such occasions.
Abdu’l-Baha and Shoghi Effendi after Him have gradually unfolded the institutional significance of this injunction. Abdu’l-Baha emphasized the importance of the spiritual and devotional character of these gatherings. Shoghi Effendi, besides further elaborating the devotional and social aspects of the Feast, has developed the administrative element of such gatherings and, in systematically instituting the Feast, has provided for a period of consultation on the affairs of the Baha’i community, including the sharing of news and messages.
(The Universal House of Justice: Aqdas: Notes, p. 202)

Devotional Portion:
During the devotional part of the Nineteen Day Feast any part of the writings of the Bab, Baha’u’llah and the Master can be read, also from the Bible and Qur’an, as these are all sacred scriptures. This part of the meeting need not be confined to prayers, though prayers can and should be read during it.
(Shoghi Effendi: Nineteen Day Feast, p. 449)

With regard to your question concerning the use of music in the Nineteen Day Feasts, he wishes you to assure all the friends that he not only approves of such a practice, but thinks it even advisable that the believers should make use in their meetings of hymns composed by Baha’is themselves, and also of such hymns, poems and chants as are based on the Holy Words.
(Shoghi Effendi: Nineteen Day Feast, p. 448)

Consultative Portion:
The chief opportunity which the friends have for discussion on administrative questions is during the Nineteen Day Feasts, at which time the members of the assembly can meet with the body of the believers and discuss in common the affairs of the Cause, and suggest new policies and methods.
(Shoghi Effendi: Dawn of a New Day, p. 201)

Now with reference to your last dear letter in which you had asked whether the believers have the right to openly express their criticism of any Assembly action or policy: it is not only the right, but the vital responsibility of every loyal and intelligent member of the Community to offer fully and frankly, but with due respect and consideration to the authority of the Assembly, any suggestion, recommendation or criticism he conscientiously feels he should in order to improve and remedy certain existing conditions or trends in his local Community, and it is the duty of the Assembly also to give careful consideration to any such views submitted to them by any one of the believers. The best occasion chosen for this purpose is the Nineteen Day Feast, which, besides its social and spiritual aspects, fulfils various administrative needs and requirements of the Community, chief among them being the need for open and constructive criticism and deliberation regarding the state of affairs within the local Baha’i Community.
But again it should be stressed that all criticisms and discussions of a negative character which may result in undermining the authority of the Assembly as a body should be strictly avoided. For otherwise the order of the Cause itself will be endangered, and confusion and discord will reign in the Community.
(Shoghi Effendi: Nineteen Day Feast, p. 452)

Who May Participate in Feast:
…a Baha’i should certainly not invite a non-Baha’i to attend [Feast].
(The Universal House of Justice: Lights of Guidance, p. 242)

As to visitors to a Nineteen Day Feast, Baha’is from anywhere in the world should of course be warmly welcomed, and may take part in consultation. However, only members of the local community can vote on recommendations to the Local Spiritual Assembly.
(The Universal House of Justice: Lights of Guidance, p. 241)