Nginx pass delete method to laravel

I'am trying to deploy simple example from here http://ift.tt/1zaE2gx. I'am using laravel 5.4.15 with homestead. Everything works fine. My code - http://ift.tt/2mObQlb. After deploying on remote web server I have 2 problems:

1.When deleting comment I get MethodNotAllowedHttpException. Seems like my nginx can't pass DELETE.

Part of my config

server{

  listen 80;

  server_name exampleName.tk

 root /var/www/blog2/public;


  index index.php index.html  index.htm;  

       location / {
        try_files $uri $uri/ /index.php?$query_string;
    }


    location = /favicon.ico { access_log off; log_not_found off; }
    location = /robots.txt  { access_log off; log_not_found off; }

    access_log off;
    error_log  /var/log/nginx/angular.app-error.log error;

    sendfile off;

    client_max_body_size 100m;

      location ~ \.php$ {
    fastcgi_split_path_info ^(.+\.php)(/.+)$;
    fastcgi_pass unix:/run/php/php7.0-fpm.sock;
    include snippets/fastcgi-php.conf;
    fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;

        fastcgi_intercept_errors off;
        fastcgi_buffer_size 16k;
        fastcgi_buffers 4 16k;
        fastcgi_connect_timeout 300;
        fastcgi_send_timeout 300;
        fastcgi_read_timeout 300;    

  }  

   location ~ /\.ht {
        deny all;
    }
}

I'm trying to make it max similar to Homestead nginx config.

server {
    listen 80;
    listen 443 ssl http2;
    server_name angular.app;
    root "/home/vagrant/Code/blog2/public";

    index index.html index.htm index.php;

    charset utf-8;

    location / {
        try_files $uri $uri/ /index.php?$query_string;
    }

    location = /favicon.ico { access_log off; log_not_found off; }
    location = /robots.txt  { access_log off; log_not_found off; }

    access_log off;
    error_log  /var/log/nginx/angular.app-error.log error;

    sendfile off;

    client_max_body_size 100m;

    location ~ \.php$ {
        fastcgi_split_path_info ^(.+\.php)(/.+)$;
        fastcgi_pass unix:/var/run/php/php7.1-fpm.sock;
        fastcgi_index index.php;
        include fastcgi_params;
        fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;

        fastcgi_intercept_errors off;
        fastcgi_buffer_size 16k;
        fastcgi_buffers 4 16k;
        fastcgi_connect_timeout 300;
        fastcgi_send_timeout 300;
        fastcgi_read_timeout 300;
    }

    location ~ /\.ht {
        deny all;
    }

    ssl_certificate     /etc/nginx/ssl/angular.app.crt;
    ssl_certificate_key /etc/nginx/ssl/angular.app.key;
}

2.

via Chebli Mohamed