At an Extraordinary Form Missa Cantata, the choir (or congregation) are expected to sing the Ordinary of the Mass (Kyrie, Sanctus, Benedictus, Agnus Dei) and the Propers, Introit, Gradual, Tract, Sequence, Offertory, Communion. Even if all these texts are sung recto tono their inclusion is mandatory. In the ordinary form, I do not think it should be any different. All the chant is there in the Graduale Romanum, the only difference is there is an Alleluia (something I find very strange for a Mass which is not of a celebratory nature), which you can however still substitute for the Tract. The Sequence, the Dies Irae, may have been removed from the Ordo of the 1970 Mass but it has not been banned. It can still be sung in its customary place before the Gospel. If you are going to sing it, you have to sing the entire thing, all nineteen verses! Just be careful you do not start singing it too low or you will be in serious trouble by the end.
If you are looking for additional music to sing, Tom Windsor from St Bede’s Clapham has sent me a link to a couple of pieces suitable for Requiem Masses found on his invaluable website. Congregati sunt and Languentibus. It is worth mentioning that you should not need to sing anything additional at the Offertory. The Domine Jesu is the longest of all the Offertory chants because it retains its verses.
There are no hymns in the Office for All Souls.
The additional psalm verses (Psalm 129, De Profundis) for the Communion Proper Lux Aeterna can be found on the Musica Sacra website HERE. Note the Gloria Patri doxology is not sung on All Souls.
There are thousands of settings of the Nunc Dimittas. A selection on Choral Wiki HERE.
Finally, the In Paradisum is only sung if there is a body, it is sung as the coffin is being taken out of the church. Hopefully, there won’t be any bodies at our Missa Cantata this evening so as we won’t be singing it, I’ll leave you with a recording of Durufle’s wonderful setting of In Paradisum.