It should call acme.sh and it will check if they need renewing, doing so if necessary.
You can check. crontab -l
You don't want to restart nginx, it will drop all active connections. You just need to reload it. Also, you only renew the certificate every two months, there is no point in reloading nginx twice a day because of this.
Yes, but it can be cleaner. You could put a copy of the certificate in /etc/nginx/ssl or someplace similar.
Yes, the command Neil gave you does exactly this. I was thinking of two more options, --fullchain-file and --key-file