Nginx fresh install configuration

I've just installed nginx on my server; now I can see with

ps aux | grep nginx

that it is in execution with my user (is this correct or should it run with root?);
anyway I'm not able to do anything with it, cannot stop it for example since

nginx -s stop

outputs:

nginx: [alert] could not open error log file: open() 
"/var/log/nginx/error.log" failed (13: Permission denied)
2017/05/02 04:03:34 [warn] 2482#2482: the "user" directive makes sense 
only if the master process runs with super-user privileges, ignored in 
/etc/nginx/nginx.conf:2
2017/05/02 04:03:34 [notice] 2482#2482: signal process started
2017/05/02 04:03:34 [error] 2482#2482: open() "/var/run/nginx.pid" 
failed (2: No such file or directory)

I've googling around about these warnings and errors, but I can't really understand them; can someone please explain:

• the meaning of the log file warning and the .pid file error
• if nginx should run with my user or with root (or something else)

UPDATE:

I'm using ubuntu server 16.04 (xenial) and I've installed nginx adding

deb http://nginx.org/packages/ubuntu/ xenial nginx

to sources.list and then

sudo apt-get install nginx

UPDATE 2

Trying to stop nginx with "sudo" still leads to error:

nginx: [error] open() "/var/run/nginx.pid" failed (2: No such file or directory)

anyway I am also confused about why

ps aux | grep nginx

shows the process running under my user (but it is not possible to kill it using the PID, and every time I run the command the PID is different)

UPDATE 3

running

nginx -t

outputs:

nginx: [alert] could not open error log file: open() 
"/var/log/nginx/error.log" failed (13: Permission denied)
2017/05/02 15:32:53 [warn] 8535#8535: the "user" directive makes sense 
only if the master process runs with super-user privileges, ignored in 
/etc/nginx/nginx.conf:2
nginx: the configuration file /etc/nginx/nginx.conf syntax is ok
2017/05/02 15:32:53 [emerg] 8535#8535: open() "/var/run/nginx.pid" 
failed (13: Permission denied)
nginx: configuration file /etc/nginx/nginx.conf test failed