One of the liturgical books in the Roman Rite of the Catholic Church is “Pastoral Care of the Sick”. It has “Part II Pastoral Care of the Dying”. An edition is at
amazon.com/Pastoral-Care-Sick-Bilingual-Edition/dp/0899421660 .
It includes:
“162. … The words “priest”, “deacon,” and “minister” are used advisedly. Only in those rites which must be celebrated by a priest is the word “priest” used in the rubrics (that is, the sacrament of penance, the sacrament of anointing of the sick, the celebration of viaticum within Mass). Whenever it is clear that, in the absence of a priest, a deacon may preside at a particular rite, the words “priest or deacon” are used in the rubrics. Whenever another minister is permitted to celebrate a rite in the absence of a priest or deacon, the word “minister” is used in the rubrics, even though in many cases the rite will be celebrated by a priest or deacon.”
Viaticum Outside Mass can be done by an Extraordinary Minister of Holy Communion (or a priest or deacon).
Prayers for a dying person are called “Commendation of the Dying”. It has “214. … The prayers are best said in a slow, quiet voice, alternating with periods of silence. If possible, the minister says one or more of the brief prayer formulas with the dying person. These may be softly repeated two or three times.” The texts are flexible. It lists some but has “or others may be added”.
Short texts are Romans 8:35, Romans 14:8, 2 Corinthians 5:1, 1 Thessalonians 4:17, 1 John 3:2, 1 John 3:14, Psalm 25:1, Psalm 27:1, Psalm 27:13, Psalm 42:3, Psalm 23:4, Matthew 25:34, Luke 23:43, John 14:2-3, John 17:24, John 6:40, Psalm 31:5a, Acts 7:59, “Holy Mary, pray for me.”, “Saint Joseph, pray for me.”, “Jesus, Mary, and Joseph assist me in my last agony.”
Readings are: Job 19:23-27a, Psalm 23, Psalm 25, Psalm 91, Psalm 121, 1 John 4:16, Revelation 21:1-5a, 6-7; Matthew 25:1-13, Luke 22:39-46, Luke 23:44-49, Luke 24:1-8, John 6:37-40, John 14:1-6, 23, 27.
Litany of the saints. There is a long form and short form.
There are five prayers of commendation, some of which may be said when the moment of death seems near. One of them is well known “Hail, holy Queen”.
There are six prayers after death, one or more may be said.
There are two prayers for family and friends, one of which may be said.
The rubrics of n. 222 include: “For the solace of those present the minister may conclude these prayers with a simple blessing or with a symbolic gesture, for example, signing the forehead with the sign of the cross. A priest or deacon may sprinkle the body with holy water.”
Chapter VII is Prayers for the Dead. This is for a situation in which the minister is called to attend a person who is already dead.
Regarding the issue of the sacraments for a Methodist, from
vatican.va/roman_curia/pontifical_councils/chrstuni/general-docs/rc_pc_chrstuni_doc_19930325_directory_en.html :
“130. In case of danger of death, Catholic ministers may administer these sacraments when the conditions given below (n. 131) are present. In other cases, it is strongly recommended that the diocesan Bishop, taking into account any norms which may have been established for this matter by the Episcopal Conference or by the Synods of Eastern Catholic Churches, establish general norms for judging situations of grave and pressing need and for verifying the conditions mentioned below (n. 131).135 In accord with Canon Law,136 these general norms are to be established only after consultation with at least the local competent authority of the other interested Church or ecclesial Community. Catholic ministers will judge individual cases and administer these sacraments only in accord with these established norms, where they exist. Otherwise they will judge according to the norms of this Directory.
131. The conditions under which a Catholic minister may administer the sacraments of the Eucharist, of penance and of the anointing of the sick to a baptized person who may be found in the circumstances given above (n. 130) are that the person be unable to have recourse for the sacrament desired to a minister of his or her own Church or ecclesial Community, ask for the sacrament of his or her own initiative, manifest Catholic faith in this sacrament and be properly disposed.137”