The answers really depend on the specific religion, but successful modern religions have evolved to protect their core propositions from testing or falsifiability. For example, if the Christian god is outside of space and time, then we cannot inspect that supposed realm to determine no god is there. That experiment can't be run, at least for the foreseeable future.
Approaching claims from the ground up is the hallmark of science; it's the empirical epistemology. As an atheist, this is how I approach everything I believe or might become convinced of. For that reason, I can't believe most metaphysical claims because I don't see how we can substantiate metaphysical claims using ground-up evidence. In contrast to many Christians who accept unfalsifiable claims because no one can disprove them, I and most atheists reject claims that have not yet been confirmed by sufficient evidence. If someone values believing as many true things and as few false things as possible, then I think my approach is the better one.
I wish all religious people would do an objective external analysis of their beliefs. Heck, non-religious people should as well. I think a good tool to use is the outsider test for faith as described by John Loftus. Examine what your religious beliefs are, and why, and then mentally swap out those beliefs for some other potential claim that is supported by an equivalent quality and quantity of evidence. If you wouldn't believe that other claim, then why do you accept your own religious beliefs? The YouTube channel "Pinecreek" does this to good effect using the hypothetical story of the Flying Man, who flew over the Grand Canyon hundreds of years ago, and some anonymous diaries were left claiming he did so, which also state that 500 people witnessed it, etc. He adds one claim after another, mirroring the supposed evidence for the resurrection, and checks whether they'd believe it yet. It is fascinating to watch how many Christians say they wouldn't accept this claim, even if all the evidence were functionally equivalent to what justifies their belief in the resurrection of Jesus.
When talking to theists, I've noticed that a lot of them don't seem to hold their faith for evidentiary reasons. Rather, they were indoctrinated at a young age and have become dependent on their beliefs for their feelings of self-worth, life purpose, and hope for the future. It is what they need to feel like the world is intelligible. It's hard to argue someone out of such beliefs using evidence, when they would have to go through the emotional work of knocking this all down and rebuild it from scratch. I suppose this is true of everyone's worldview to some extent, even atheists, but our views are arrived at through open inquiry and freedom to doubt. I think that leads to a stronger foundation, with a stronger justification. When I only accept claims that can be reliably demonstrated, then I'm not attaching emotional reliance to things that likely aren't real, and I don't have to do the constant work of propping up imaginary notions just so I can get through my day.
So go ahead. Ask questions. Run some thought experiments. If your beliefs are true and justified then this approach can only strengthen them.
