Should I close the Nginx process ? (80 port)
It depends which method you are using ( and which client). I tend to leave nginx ( or apache) running, and renew the SSL without taking down the running web service at all.
The rest of the time I don’t close port 80 either, although I do divert the bulk of the traffic to https ( port 443)
Install it manually the first time and by using webroot authentication from there on out to avoid taking your site(s) down you should be good to go.