What are the correct volume maps for zabbix running on Docker?
There is a list of all the important paths Zabbix containers use: https://www.zabbix.com/documentation/3.0/manual/installation/containers 
(scroll down a bit until you find "Volumes" part). 

If I were you, instead of bind mounting these directories I would build a derivative image from the official Zabbix image and run statements like "COPY my_alertscript.sh /var/lib/zabbix/alertscripts/" in the build phase. 

If, for some reason, baking your changes to the image itself is not possible, then you may still want to prefer named volumes instead of bind mounting. See: https://docs.docker.com/storage/volumes/ to read about its advantages.