Hi! I'm a relatively new buddhist and I have never had a proper understanding of 3 things because of the specific school/teachings research I've done. If you could clarify or explain any of these then I would be greatly indebted to you.
Mantras and how and why and for what they're used
Practicing reliance on buddhas and bodhisattvas
The role of prayers
These are all good questions and big questions. The general answer to all of these: mantras, devotional practices, and prayers are all used because they are useful as practices. They are meditation practices in their own right, and they accomplish something if you practice properly. What that "something" is, and how it is said to be done, will depend on your situation and your intentions and aspirations. You will get different explanations depending on the tradition you are working in, for instance.
Mantra practice is generally something you need personal instruction in before you can proceed. There's an oral transmission involved from teacher to student. There are a few exceptions to this, however. Anyone can recite OM MANI PEME HUM, for example. That's a popular one.
One purpose of reciting prayers is to cultivate certain aspirations: for instance, to practice Dharma more effectively, to live a long time so you can have time to practice, and so on. There are many, many, many of these.
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