In general the decisions about who does what are made by the Parish Priest, following the General Instruction of the Roman Missal:
“107. Liturgical functions that are not proper to the Priest or the Deacon and are mentioned above (nos. 100-106) may even be entrusted by means of a liturgical blessing or a temporary deputation to suitable lay persons chosen by the pastor or the rector of the church.[footnote 89 …] As to the function of serving the Priest at the altar, the norms established by the Bishop for his diocese should be observed.”
Doing the readings is the best documented I have found. Perhaps it would guide the Parish Priest in deciding the other functions. From the General Instruction of the Roman Missal:
“99. The lector is instituted to proclaim the readings from Sacred Scripture, with the exception of the Gospel.”
Only men can be instituted as lectors, not women. No one should be ordained as a Deacon or Priest unless he has been instituted as a lector.
“101. In the absence of an instituted lector, other lay people may be deputed to proclaim the readings from Sacred Scripture ….”.
Regarding non-Catholics there is the “DIRECTORY FOR THE APPLICATION OF PRINCIPLES AND NORMS ON ECUMENISM” at http://www.vatican.va/roman_curia/pontifical_councils/chrstuni/documents/rc_pc_chrstuni_doc_25031993_principles-and-norms-on-ecumenism_en.html
It discusses how non-Catholic Christians can participate in Catholic ceremonies and vice-versa.
Under the heading
“Sharing in Sacramental Life, especially the Eucharist
a) Sharing in Sacramental Life with members of the various Eastern Churches”
“126. Catholics may read lessons at a sacramental liturgical celebration in the Eastern Churches if they are invited to do so. An Eastern Christian may be invited to read the lessons at similar services in Catholic churches.”
Under the heading:
“b) Sharing Sacramental Life with Christians of Other Churches and Ecclesial Communities”
“133. The reading of Scripture during a Eucharistic celebration in the Catholic Church is to be done by members of that Church. On exceptional occasions and for a just cause, the Bishop of the diocese may permit a member of another Church or ecclesial Community to take on the task of reader.”
[Excerpts from The Roman Missal © 2010, International Commission on English in the Liturgy Corporation. All rights reserved.]