On singing, from the General Introduction to the Lectionary:
“14. A speaking style on the part of the readers that is audible, clear, and intelligent is the first means of transmitting the word of God properly to the assembly. The readings, taken from the approved editions,
[footnote 28: See no. 111 of this Introduction.]
may be sung in a way suited to different languages. This singing, however, must serve to stress the words, not obscure them. On occasions when the readings are in Latin, they are to be sung to the melody given in the Ordo cantus Missae.
[footnote 29: See Missale Romanum ex Decreta Sacrosancti Oecumenici Concilii Vaticani II instauratum, auctoritate Pauli Pp. VI promulgatum, Ordo cantus Missae (ed typ., 1972), Praenotanda, nos. 4, 6, 10.]”
Standing for the Gospel, from the 2002 General Introduction to the Roman Missal (GIRM) approved for the USA, which can be accessed from romanrite.com/girm.html :
“43. The faithful should stand from the beginning of the Entrance chant, or while the priest approaches the altar, until the end of the Collect; for the Alleluia chant before the Gospel; while the Gospel itself is proclaimed; …”.
"60. The reading of the Gospel is the high point of the Liturgy of the Word. The Liturgy itself teaches that great reverence is to be shown to it by setting it off from the other readings with special marks of honor: whether the minister appointed to proclaim it prepares himself by a blessing or prayer; or the faithful, standing as they listen to it being read, through their acclamations acknowledge and confess Christ present and speaking to them; or the very marks of reverence are given to the Book of the Gospels."
From the Ceremonial of Bishops:
“Reverence toward the gospel
74 While the gospel reading is being proclaimed at Mass, at a celebration of the word, and at a prolonged vigil, all stand and, as a rule, face the reader.”
(Ceremonial of Bishops, Liturgical Press, 1989, ISBN 0-8146-1818-9, page 37).
On lay people proclaiming the Gospel on Good Friday, from the Roman Missal:
“8. Finally the account of the passion according to John (18:1-19:42) is read, in the same way as on the preceding Sunday.”
For Passion Sunday (Palm Sunday) it has:
“The passion is read by the deacon or, if there is no deacon, by the priest. It may also be read by lay readers, with the part of Christ, if possible, reserved to the priest.”
(Roman Missal, Catholic Book Publishing Co., New York, 1985, page 126.)
The Latin text in the 2002 Roman Missal for this rubric is:
“Legitur autem a diacono vel, ipso deficiente, a sacerdote. Legi potest etiam a lectoribus, parte Christi, si fieri potest, sacerdoti reservata.”
(Missale Romanum, Libreria Editrice Vaticana, 2002, ISBN: 8820972719, page 281).
The Ceremonial of Bishops does not envisage this. It has, “319 … Neither incense nor candles are used for the narrative of the passion. The deacons who are to proclaim it ask for and receive a blessing from the bishop in the usual way.”
(Ceremonial of Bishops, Liturgical Press, 1989, ISBN 0-8146-1818-9, page 108-109).
Women reading the Passion when there are 20 priests is wrong because of the exceptional nature of the permission for lay people to read the Passion in the liturgy. The Ceremonial of Bishops assumes there will be enough deacons, it does not make the provision for priests, or lay people to do this.
The idea of some people being able to do the job of others only in their absence is expressed in the GIRM with:
"101. In the absence of an instituted lector, other laypersons may be commissioned to proclaim the readings from Sacred Scripture."
Also in the Introduction to the Book of Blessings:
“An acolyte or reader who by formal institution has this special office in the Church is rightly preferred over another layperson as the minister designated at the discretion of the local Ordinary to impart certain blessings. …
But whenever a priest or a deacon is present, the office of presiding should be left to him.”
(Book of Blessings, Liturgical Press, Minnesota, 1989, ISBN 0-8146-1875-8, page xxviii, n. 18).