JOEL - I wouldn't call these things "rules" or "myths"; they are just expressions of respect and reverence that should be observed to preserve the sacred and holy meaning of the ordinance.
For example using the right hand has always been practiced when performing any priesthood ordinance, including the temple ordinances.

President Joseph Fielding Smith said:
"The performing of ordinances with the right hand in preference to the left is a well-established custom universally and is not confined to the Church. In various governments where oaths are administered, the candidate for office is asked to raise his right hand. There are occasions when he is sworn to give truthful testimony by placing his right hand on a copy of the Bible. This custom has come down from the beginning, and from many scriptural passages we gather that it has always received divine sanction. When Abraham sent his servant to his kindred to find a wife for Isaac, he had the servant place his right hand under Abraham's thigh and swear to him that he would accomplish this mission.(Genesis 24:2. ) There are other occasions of similar import. One of the earliest incidents recorded is the blessing Jacob gave his grandsons, Manasseh and Ephraim. Manasseh was the elder, and as Joseph presented his sons to their grandfather, he presented Manasseh towards Jacob's right hand and Ephraim towards his left hand. The record states that Jacob "guiding his hands wittingly" placed his right hand on the head of Ephraim and his left hand on the head of Manasseh. Joseph protested, saying, "Not so, my father: for this is the firstborn; put thy right hand upon his head."
"I know it, my son, I know it:" said Jacob, "he also shall become a people, and he also shall be great: but truly his younger brother shall be greater than he, and his seed shall become a multitude of nations."(Answers to Gospel Questions).

And he also said: "It is the custom to extend the right hand in token of fellowship. The right hand is called the dexter, and the left, the sinister; dexter means right and sinister means left. Dexter, or right, means favorable or propitious. Sinister is associated with evil, rather than good, Sinister means perverse. We take the sacrament with the right hand. We sustain the authorities with the right hand. We make acknowledgment with the right hand raised." (Doctrines of Salvation, Vol.3, p.108)

The showing favor to the right hand or side is not something invented by man but was revealed from the heavens in the beginning. To Isaiah the Lord said:
"Fear thou not; for I am with thee: be not dismayed; for I am thy God: I will strengthen thee; yea, I will help thee: yea, I will uphold thee with the right hand of my righteousness. . . .For I the Lord thy God will hold thy right hand, saying unto thee, Fear not; I will help thee." (Isaiah 41:10, 13.)

And:

Hearken unto me, O Jacob and Israel, my called; I am the first, I am also the last.Mine hand also hath laid the foundation of the earth, and my right hand hath spanned the heavens: when I call unto them, they stand up together.(Isaiah 48: 12-13.)

In the Psalms we read:
"The Lord said unto my Lord, Sit thou at my right hand, until I make thine enemies thy footstool.(Psalm 110:1; Matthew 22:44.)

The Lord, in speaking to his disciples, shortly before his death, said unto them:
"When the Son of man shall come in his glory, and all the holy angels with him, then shall he sit upon the throne of his glory:And before him shall be gathered all nations: and he shall separate them one from another, as a shepherd divideth his sheep from the goats:And he shall set the sheep on his right hand, but the goats on his left.Then shall the King say unto them on his right hand, Come, ye blessed of my Father, inherit the kingdom prepared for you from the foundation of the world:" (Matt 25:31-34)

President George Albert Smith said:
"Our people have been taught to take the sacrament with the right hand; we believe that is appropriate, and proper, and acceptable to our Father. The sacrament should not be accepted with a gloved hand; nobody should receive it in that irreverent manner. We should partake of it in humility, with preparation of clean hands and pure hearts, and with a desire to be acceptable to our Father; then we will receive it worthily, and rejoice in the blessing that comes to us by reason of it." (Conference Report, April 1908, p.36)

The entire Sacrament ordinance includes from the moment the bread is broken until the the last cup of water is taken. If one does not participate in the whole thing the ordinance is not complete. You would not walk into a temple endowment session half way through or baptize someone without saying the baptismal prayer.
The same with the Sacrament ordinance. The two sacrament prayers are a little different, where in the first we are reminded to take upon ourselves the name of Christ and to keep the commandments, while in the second that reminder is not there. So if we miss the bread we have missed that part of the covenant we are suppose to make when we take the sacrament.
There is nothing really published about the other so-called "rules", they are simply signs of respect and to keep things orderly and to prevent distraction.