Error 404 converting .htaccess to web.config

My web server is IIS, so my .htaccess files don't work. Could you help me with the redirection and hiding the filename extension? My code gets a 404 error. I have two web.config files.

original .htaccess (1):

Options -MultiViews
RewriteEngine On
Options -Indexes

RewriteCond %{REQUEST_FILENAME} !-d
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-l
RewriteRule ^(.+)$ index.php?url=$1 [QSA,L]

web.config (1):

<?xml version="1.0" encoding="UTF-8"?>
<configuration>
  <system.webServer>
    <rewrite>
      <rules>
        <rule name="RewritePHP" stopProcessing="true">
      <match url="^(.+)$" />
      <action type="Rewrite" url="/index.php?url={R:1}" appendQueryString="true"/>
    </rule>
  </rules>
</rewrite>
 </system.webServer>
</configuration>

original .htaccess (2):

RewriteEngine on
RewriteRule ^(.*) public/$1 [L]

This web.config (2) works well (route the vhost to /public):

<?xml version="1.0" encoding="UTF-8"?>
<configuration>
  <system.webServer>
<rewrite>
  <rules>
    <rule name="rewritepublic" stopProcessing="true">
      <match url="^(.*)" />
      <action type="Rewrite" url="public/{R:1}" />
    </rule>
  </rules>
</rewrite>
  </system.webServer>
</configuration>

Details error 404:

IIS Web Core
MapRequestHandler
StaticFile
0x80070002

URL request: http://localhost:81/site/public/page1
Path: C:\inetpub\wwwroot\site\public\page1