I'm not a Roman Catholic, but I'm still a Catholic (even if Rome says otherwise), so I'll try to at least adress some of the points you have made.

Firstly, there are lots of different kinds of prayer in the Christian Tradition:

• Liturgical (special prayers in a ritualized setting)
• Praise/Thanksgiving/Adoration (these are all separate, but there's lots of similarities)
• Meditative/Contemplative (there's a fine distinction between these two that we don't need to go into)
• Supplication (asking God for something for oneself)
• Intercession (asking God for something for others)

There are others, and they can be divided up in different ways (Liturgical Prayer is a very broad category), but the general point is that most people tend to focus solely on the second two, which are only a part of the wider practice of prayer.

The answer to your question hinges on:

I'm pretty sure some religions, including Christian branches, say that prayer gives you salvation.

I'm no too sure where you got this idea, but I don't think you'd find that it's mainstream in Christianity (what with it being pretty bloody heretical). Salvation in Christian thought is widely agreed upon to come from faith in God. Exactly how that manifests, how good 'works' plays into it, and the role of Jesus Christ in that (is He essential or preferable?) is debated, but I don't know of any soteriological (the study of salvation) branch that has prayer as 'giving Salvation'.

Presumably your question hinges on the tension between 'everything is God's Plan' and 'Prayer changes things'?

Firstly, we should recognize that this isn't necessarily a meaningful question for all kinds of prayer (if the point of contemplative prayer is to simply contemplate God, then I don't think the question really applies to it).

As to the interplay of intercessory prayer and 'God's plan', there are many different answers. How I imagine a 'good' Catholic would respond would be soemthing like:

'God has a plan for all things. But often this plan is enacted through the Church as the continuing Body of Christ. As prayer calls to mind that which we need to do, focuses our minds and hearts on those issues, and asks for God's help in that, there is no necessary contradiction between the result of prayer and God's Plan'.

In short, prayer doesn't have to be askign God to act as an external agent that 'reaches down' and abrogates natural laws. Rather, it can be about effecting an internal change within the prayer-giver, that better focuses us on the 'plan of God' and sets us up to go out and try to realise God's plan in the world today.

Prayer isn't about asking God to act against His plan. It's about establishing a relationship with God through which we can effect God's plan.