The hukou explained, for Singapore applications
The household register, or hukou, is asked for because of what it proves rather than what it says. For many applicants it is the only documentary evidence of a family relationship that an authority will accept.
What it is
A booklet recording a household: who belongs to it, and how each person relates to the head of it. It is maintained over years, often by hand, and it carries stamps, corrections and annotations that are part of the record rather than clutter around it.
The relationship field is the point
The entry recording each member as son, daughter, spouse, mother or grandparent of the head of household is what the reader is actually looking at. These terms are precise in Chinese and vague in careless English.
A translation that flattens them into relative has destroyed the only thing the document was produced to prove.
Which pages to send
Usually the index page plus the page for every member named in your application. A single page proves nothing about a household, which is why partial sets come back.
Check with whoever is receiving it, because translating a subset and then being asked for the rest costs more than doing it once.
Handwriting and amendments
Booklets updated over decades are normal. Annotations, corrections and stamps are reproduced in place and described where they cannot be typed, and anything genuinely illegible is marked as such rather than guessed at.