Hi there,
First of all about the registration you’ve to enable registration from the settings->general tab of your dashboard. Select anyone can register & that’ll enable registration on your site.
About google map where are you putting the api key. There are option to set api key in theme option don’t know what’s causing issue. Can you be more specific on your map issue I mean you can provide some screenshots of errors which you’re getting. That would help us find out a solution for you.
Regards