On Android running Marshmallow, you'll want to disable doze for WhatsApp.

For stock Android, this link shows how to do that: http://www.greenbot.com/article/2993199/android/how-to-turn-off-doze-mode-for-specific-apps-in-android-marshmallow.html

On my LG phone, I went to settings -> General Tab at the top -> Battery & power saving -> Battery Usage

Scroll down till you see Battery Optimization and under that, tap 'Ignore optimizations'

Scroll down until you see WhatsApp and move the slider so it is on.

(Partially answering my own question)

The privacy policy section Information We Collect states:

You provide us the phone numbers in your mobile address book on a regular basis, including those of both the users of our Services and your other contacts. You confirm you are authorized to provide us such numbers.

Note that last sentence that you have to agree with.

So this answers that 'we'=WhatsApp Inc collects the information from my contact list. In how far this is passed on to 'Facebook' is unclear:

WhatsApp is part of the Facebook family of companies, and sharing some information allows us to coordinate more and improve experiences across our services and those of Facebook and the Facebook family.

Update March 2018, quoting from the NakedSecurity blog by Sophos:
Facebook: we won’t share data with WhatsApp (yet)

WhatsApp can’t share user data with parent Facebook without breaking the upcoming General Data Protection Regulation (GDPR), so it won’t.

It’s signed a public commitment not to share personal data with Facebook until data protection concerns are addressed

So it seems that they don't but still want to if they can make it legally possible. No suprise there.

The blog post gives a good overview of past facts and intentions, including a reference to that March 2018 'public commitment' document signed by WhatsApp.