Re: False beliefs
It depends on whether or not those false beliefs are harmful. Plenty of people "know" trivia that is incorrect. Since it is just trivia, it's not worth my time to correct them.
Personally, I believe that Bigfoot and the Loch Ness monster exist (I imagine you don't). I know, logically, they may not. Since I am not wasting time (well, maybe watching a few you tube videos or looking at websites) or resources trying to track them down, or using that belief engage activities harmful to myself, family, or others, I'm sure you would agree my belief is harmless. You probably wouldn't waste your time trying to convince me they don't exist.
Now when prayer is used INSTEAD of using known solutions, it can be harmful. Such as rejecting medical treatment in favor of praying. However, praying in addition to medical treatment causes no harm.
Prayer is also used when people cannot actually do anything to help. "Sending prayers" is essentially sending sympathy.