the issues is not whether you believe this or not, but rather whether following this path you can attain the ending of suffering. the approach is different from other 'religions'.
as to the how true these supernormal powers are there are suttas suggesting that these things actually happen and other suggesting that they are in the mind of the person 'doing' them. There are second hand stories of people who are able to do these things as well. The truth of this matter is not important for the ending of suffering.