For the spirit world, right?
Questions and experiments - for example,
Is the Bible reliable, accurate, and authentic? Can it be trusted?
Is it reasonable to conclude that there is a creator / designer?
Does the evidence meet our expectations, of what would be true?
... and many more related questions.
But what method are you using to find answers to those questions re: the spirit world, if it isn't science? How would we determine that what the Bible says about "the spirit world" is accurate?
Observations
(Romans 1:19, 20) 19 ... what may be known about God is clearly evident among them, for God made it clear to them. 20 For his invisible qualities are clearly seen from the world’s creation onward, because they are perceived by the things made. . .
Which observations have been made of the spirit world?
If the Bible can be trusted, as the word of God, then it serves as a measuring rod for truth.
(2 Timothy 3:14-17) 14 You, however, continue in the things that you learned and were persuaded to believe, knowing from whom you learned them 15 and that from infancy you have known the holy writings, which are able to make you wise for salvation through faith in Christ Jesus. 16 All Scripture is inspired of God and beneficial for teaching, for reproving, for setting things straight, for disciplining in righteousness, 17 so that the man of God may be fully competent, completely equipped for every good work.
How do you non-scientifically determine if the Bible can be trusted?
Weight or test the 'knowledge'.
What does this mean? You seem to be using scientific terminology: observation, testing, etc. But this is a non-scientific process you're describing? How would you non-scientifically test something?
Follow the evidence where it leads.
Evidence collected how? How does one collect evidence of spirits?
How do you determine that your beliefs are accurate?
Empirically testing them. So for example, if I believe I have $5 in my pocket, I test that by looking in my pocket and seeing if I have US currency in there totalling $5.
Believing that a theory is accurate does not allow you to determine that your interpretation of the 'results" are accurate.
Our results may also be interpreted as accurate.
This is one reason why in science we make predictions ahead of time when we plan to test hypotheses. Post hoc rationalization is too easy.
Where does proof comes in? Can any of us absolutely prove anything?
I don't think we have absolute proof of pretty much anything. We have evidence that leads us to probabilistic conclusions about what is more or less likely to be the case.