Christ is in our midst!
This particular greeting is traditionally used only by priests greeting each other. It is not commonly used by laymen.
1) Is there a distinction to be made between Akathists and Canons? I'm obviously not referring to the canon law, but various canons that are found in prayer books, etc.
2) When are they to be read/chanted?
They are basically two different poetic forms.
A canon has 9 Odes (of which the 2nd is almost always omitted (except during Great Lent - the Great Canon of St Andrew is a good example) due to its penitential character., Each ode begins with an irmos and then has a number of tropari separated by a common refrains; it then ends with a katavasia. In parish practice the canon is normally part of the matins service. In Byzantine tradition there is the tradition of singing a "small supplicatory canon" to the Mother of God as an occasional service. In the Slav tradition this kind of service is more often the "molieben" (and an canon can be, but usually isn't, included in the molieben). A common "abbreviation" in the services is to sing only the irmosi (often the way matins is sung in Byzantine practice) or only the refrains (often used in the Slavic molieben).
An akathist is a poem that has 12 parts. Each part consists of a kontakion ending with the triple alleluia and an irmos with a set of refrains (it is frequently the case where the priest chants the kontakion and irmos and the alleluias and refrains are sung by the choir/people). The common structure of the akathist is that each irmos will have 12 refrains, each different, that are then followed by a single line that is the same throughout the akathist. The akathist is most often used as a part of one's personal prayers or can be sung as an occasional service in Church. Example: When the Kursk Icon recently made the rounds in the diocese, there would always be an akathist to the Virgin sung before the icon in Church as a public service. A short molieben (with no canon) would be sung at each home where the icon was brought to bless the house.
3) Why are they to be read/chanted?
They are used as prayers - either as a part of one's personal prayers or incorporated in the communal prayers (services) of the Church. I will sometimes "prescribe" the reading of an akathist to someone who is having a particular difficulty in their lives as a spiritual aid. I have seen, for example, severe depression turned back with the daily reading of the akathist to the Mother of God.
4) In the Jordanville prayer book, it asks the pious Christian to read three canons (I think, I don't have it in front of me) as preparation for communion. Is this on top of the "order of preparation for holy communion?" Is this something to aspire to? Because my discipline is simply not there yet. It would be my assumption that there's not a "one size fits all" kind of thing?
The standard preparation for receiving communion in the Russian Church is to read three canons (Savior, Virgin, Guardian Angel) and one akathist (usually the Mother of God or the Savior - but there are others that can be used as well) the evening before one receives. These canons and akathist can be combined into a single unit and in the Jordanville Horologion such a service can be found (it can also be found and purchased in a separate booklet). This combination service is sometimes read aloud in Church prior to the beginning of the All-Night Vigil for those who are preparing to receive the next day. Then the morning that one receives a person will read the service of preparation which consists of psalms, troparia and a short canon followed by a standard set of prayers (about 10) culminating with the set of prayers "I believe O Lord and I confess ..." that is said in the Liturgy when the Gifts are presented. Now keep in mind that in the Russian Church most people receive the Mysteries once or twice a year - the more pious receiving 4x a year with each fasting period. For those who receive more frequently the rule can be lessened.
5) Who arranged the prayers that we have in most of our prayer books? How was it determined that these are the prayers to be said in the morning, in the evening, before communion, etc.?
The prayers were arranged by our old friend "tradition" - most likely based on monastic or clerical practice. Keep in mind that general literacy was not common until after WWII (mid 20th century) and so written prayer books and prayer rules were not commonly used by the laity except by those who could read. Akathists and Canons, because they were poetic forms and were often sung, were more easily memorized and thus could be more easily learned and used by someone who was unable to read prayers from a book.