Yes, sometimes they are interchangeable, but in most cases they are not.
They are different as to their subject.
Back up is usually used of a person, but could be used of the story, testimony, evidence presented by the person.
Bear out is almost always used of the evidence, testimony etc, not of the person presenting it. (but see * below)
So only back up is possible for your 3, 4, 5, 6. Either may be used for 1 and 2 (but in my view, bear out indicates a more complete support than back up).
Added in an edit:
*There is an exception: the phrase bear me out does seem to be used with people as the subject (I think it can almost be regarded as an idiom).
The BNC (British National Corpus) has
- three examples of bear me out, all with a person as the subject,
- one example of bear him out, with 'records' as the subject
- only three out of about 50 examples of bear out have a human subject.
In COCA (the Corpus of Contemporary American English),
- eight out of eleven instances of bear me out have a human subject
- only one of twenty instances of bear him out has a human subject, and
- possibly two of about 130 instances of bear out have a human subject (possibly two because the context isn't quite clear from the extract).
[I've also changed "always" to "almost always" above, because this data does show that it is occasionally used with a human subject even apart from the idiom bear me out.]