Just for a starting point, I looked in an older book, the recently republished Parish Ritual (from pcpbooks.com) to see what it has for Forty Hours.

It provides instructions for the exposition and for the reposition, but nothing about what comes between.

According to that book, Forty Hours begins with:
* a votive Mass of the Blessed Sacrament
* a eucharistic procession. "Pange lingua" is sung and repeated as necessary, but the last verses -- the "Tantum ergo" -- are saved until the end of the procession. The versicle "Panem de caelo" and its response are omitted.
* The Litany of the Saints is sung, ending with Kyrie eleison/Christe eleison/Kyrie eleison.
* Pater noster
* "O God, come to my assistance" (as in the start of the Office); then psalm 69
* A dialogue of intercessions: against evil, for the mercy of God, for the Pope, for our benefactors, for the dead, the absent
* The collect of Corpus Christi ("Deus, qui nobis sub sacramento...")
* A collect invoking our Lady's intercession (varying according to the season of the year)
* Prayers for the Pope, the Church, for the conversion of heretics
* A collect for the repose of the faithful departed
* closing versicles

At the reposition, most of the same prayers are given again: first the litany, then psalm 69; then comes a procession with "Pange lingua" as before, then "Tantum ergo"; this time the versicle "Panem de caelo" is added, and the collect of Corpus Christi and the subsequent prayers. Finally, the blessing with the Sacrament is given and the Sacred Host is reposed. The Divine Praises follow.

---

The current document that provides guidance for exposition of the Blessed Sacrament is "Eucharistic Worship Outside Mass"; see paragraphs 82 and thereafter: https://www.ewtn.com/library/CURIA/CDWSACRA.HTM

It urges (para. 86): "In churches where the eucharist is regularly reserved, it is recommended that solemn exposition of the blessed sacrament for an extended period of time should take place once a year", so Forty Hours seems to fulfill a recommendation of the Church.

That on-line document isn't complete, as the text goes on to provide a list of scripture readings, hymns, penitential rites, antiphons, responsories, and collects that can be used. If your parish has a copy of the anthology "The Rites" (Pueblo Publishing), the whole document is in there. Those antiphons and responsories are just given as texts, but of course are meant to be sung: so you can take them as an invitation to sing musical settings of them.

Yes; paragraph 83 of the document says that the celebration of Mass is prohibited in the body of the church where exposition is taking place. The exposition may be interrupted, or Mass may be celebrated in a chapel distinct from the area of exposition.

On the other hand, the Liturgy of the Hours can and should be celebrated during exposition.

The liturgy office of the Bishops of England&Wales points to these resources.

In my first full-time parish the priests and I actually revived 40 Hours, which we actually did centered around our patronal feast day in October. This is what we did:

Day 1 - Sunday
Exposition would begin at the end of the final Sunday Mass (we didn't have a Sunday evening Mass) at 11:00 a.m.
Adoration continued at the main altar through the day until Vespers at 7:00 p.m. with Benediction at the end.
Adoration then continued in the side chapel, which was more secure overnight.

Day 2 - Monday
Morning Mass was celebrated at 9:00 a.m., usually a "Missa Pro Pacem" if allowed. The Blessed Sacrament was quietly reposed a few minutes beforehand, and a new host for adoration that day was consecrated, the previous day's being fractured and used with other hosts for the Communion of the faithful.
Adoration at the main altar throughout the day, Vespers/Benediction at 7:00 p.m., adoration continuing in chapel throughout the night as before.

Day 3 - Tuesday
Morning Mass at 9:00 a.m., usually a Votive Mass of the Holy Eucharist if permitted, everything above as before.
At Vespers that evening, we'd conclude with a Eucharistic procession through the streets of the town, with Benediction in the church at the end of it. Then the Blessed Sacrament was reposed and everyone went to the parish hall for a reception.

At Vespers each evening we'd often have a guest preacher, often times a priest who had served in the parish before. Since then I understand they've had a recently-ordained son of the parish, and even the diocesan bishop has come.

This really took off well when I was there, and since then I understand has become a major event not just for the parish, but for the whole town. So that's a "humble brag" of mine, that I helped get it kick-started.