On those fonts, the SBL ones appear to be Unicode-based, but I’m not sure about the other two. I’d recommend sticking to Unicode, as that’s what should come from Word.
On the Hebrew vowels, are you using World-Ready Paragraph Composer in InDesign (see any number of posts on this forum and web pages elsewhere for details)? – if not, that would account for the vowel points being out of position.
On the Bible software program, I’ve no idea how it handles text. It might require non-standard font encodings, which could also account for the left-to-right-ness of that route.
On the Greek squares, it sounds like the font being used doesn’t recognise the text – can you pin down the “sometimes” to using a particular font?
Is there a particular reason for the requirement to use those 4 fonts mentioned? If TNR works for Greek, what’s wrong with that?
Hope that’s of some help.
Good luck,
Chris