Greetings,
I agree that we are contained within our physical reality and cannot get out. This does depend on your definition of "we" (or "I") though. It also depends on whether or not there is an "after-life"; if there is, then we are contained only by being alive. There are also dualism considerations, reference Richard Swinburne.
As for our thoughts affecting the reality outside us, I would have (as my first thought) that it is more a case of the reality outside us affecting our thoughts. Imagine if your brain had no sensory inputs.
There are limitations of an evidence-based approach, but I suggest that it is the "gold standard" and has delivered a good track record. afaik, no other approach has delivered anything useful.
The issue I have with faith comes from its definition - faith is based on no evidence/data/proof. It is a case of "anything goes", that is, any version of faith is as good as any other. This comes from the impossibility of verification of the claims of any version of faith. We might be impartial here - use the same methodology and standards of evidence to analyse all versions of faith.
If, for example, a person's faith comes from upbringing, this is a case of pre-conditioning, in much the same way as pre-supposition leads to question-begging. If you are taught that a "religious experience" as it applies to your version of faith, has particular features and attributes, and you then some time later have such an experience, your pre-conditioning will "tell" you that your version of faith it true.
rgds, igr.