You can create a source-citation for the Bible, using that as source for whatever data is in it. You can include in the "detail" for the citation who the present owner is and who prior known owners were. For example, I have copies from a Bible presently in possession of a distant cousin, who was given it by one of her aunts; it has entries in several hands -- and the original owner was probably the aunt's mother, judging by the consistent handwriting for all of that mother's children's birth dates. You can then attach the Bible source-citation to the persons whose vital dates are listed.
You can use the 'story' function to create a transcript of the Bible entries together with whatever history you know about it (including publication data from the title page, if you have access to it), and then attach the 'story' to the other persons. One way to do this is create the transcript in a word-processor on your computer and save as a PDF file, which deters others from making changes if they copy your story from your tree (if it is a public tree). This you can easily upload and attach to multiple tree persons all in one operation.
If you have doubts about whether a person belongs in a family, you can use the 'suffix' field to add "possible" or whatever makes sense to you. This will not change how the name is alphabetized in your tree's "List of persons" but will appear with the person's name in the list. There is really no obvious way to 'flag' a date or place as questionable that way, but the suggestion to annotate in the "description" field is sound -- so you will see it when you look at the person's profile page.