Toward the secondary question of how Catholics approach ecumenical prayer, ecumenism is generally encouraged by the Catechism and the teaching of the bishops.
What is allowed to the faithful Catholic is to join in those spiritual activities which we can engage in together in an honest way, since the Catholic church teaches that all Christians have a real unity by way of our baptism, but also recognizes that we have real differences which have resulted in a visible separation. These activities are most commonly prayer, bible study, and praise/singing (not "worship" as Catholics define it). A Catholic may also be a reader in a non-Catholic gathering if invited. Catholics may also attend services/celebrations which are recognized as valid by the Catholic church, such as the baptism of a relative.
What is not allowed is to participate with other Christians in ways that would be dishonest. For example, in the Catholic conception of communion, when a Catholic receives the Eucharist, they are expressing that they are one with Christ as well as that they are one with the Catholic community. In most cases, the Catholic is also professing a significantly different understanding of what is happening during communion. For these reasons, a Catholic could not participate with a non-Catholic in a communion service, because what they would be "saying" by their actions would be dishonest. Catholics are also taught that it is not appropriate to participate in non-Catholic services if their intent is to seek the things they should be seeking from the Mass. So it would be illicit for a Catholic to attend a non-Catholic service instead of attending Mass in most cases.
This also highlights the differences in the structure of different Christian communities. What it means to be Catholic is to be in communion with the preaching and teaching authority of the bishop of one's diocese, which is handed down from the apostles, where the bishop is himself in communion with the bishop of Rome. However, in other churches, such as many Protestant or Orthodox national churches, there may not necessarily be universal agreement on what is expected, or there may be significantly different local interpretations of canon law or other more universal "touchpoint" documents.
This is not the main question, but I can provide references on particular points if helpful. However, it is usually best to create a separate question if you want to receive several in-depth answers with references.