score:2
Your family name is the same thing as a last name.
Your "other name" field, should only be filled in if the form explicitly asks for it, otherwise stick with first name and last (family) name.
If you have a compound first name, don't put the second part of your first name as the middle name - as this will confuse many systems.
You should fill out the form with the names as stated in your identity page, not how they are written in the MRZ area.
Do not use any nicknames or other aliases that you may be known by, and definitely don't try to "reverse engineer" your name from the MRZ.
To answer your direct question:
Is the MRZ format documented somewhere
Yes, it is in ICAO Document 9303 part 3.