Calendar and Contacts sync issue
The downside of this phone is that google play, google contacts sync and google calendar sync are not installed by default. You have to install them by yourself, you can download them for example from apkmirror (http://bfy.tw/AJnQ, http://bfy.tw/AJnR, http://bfy.tw/AJnU).
The installation of these apks is just the first part. To make the synchronization really working you need to give those applications proper rights - access contacts, calendar and make sure they they are not closed when the display is locked (battery management).
Push notifications not working
I'm not sure if I had this issue since the beginning or if it started after upgrade to Android 7.0 nougat. The problem was that after some time of locked display I was not getting messages to messenger (WhatsApp, FB Messenger).
I gave these applications different rights in applications settings and notification privileges in notifications settings and made sure they are not killed when display is off in battery saving settings, but it still didn't help.