I noticed it only recently, but maybe it's been a long time, i've only ever looked in briefly as admin. Site is 4 years old.

That's my .htaccess:

AddType application/x-httpd-php73 .php
Options +FollowSymLinks
RewriteEngine On

AddEncoding gzip .gz
AddEncoding gzip .gzip
<FilesMatch "\.(js.gz|js.gzip)$">
  ForceType text/javascript
</FilesMatch>
<FilesMatch "\.(css.gz|css.gzip)$">
  ForceType text/css
</FilesMatch>

RedirectMatch /index$ https://mysite.de
RewriteCond %{REQUEST_URI} !^/index\.php
RewriteCond %{REQUEST_URI} !/ow_updates/index\.php
RewriteCond %{REQUEST_URI} !/ow_updates/
RewriteCond %{REQUEST_URI} !/ow_cron/run\.php
RewriteCond %{REQUEST_URI} !/e500\.php
RewriteCond %{REQUEST_URI} !/captcha\.php
#RewriteCond %{REQUEST_URI} (/|\.php|\.html|\.htm|\.xml|\.feed|robots\.txt|\.raw|/[^.]*)$  [NC]
RewriteCond %{REQUEST_FILENAME} (/|\.php|\.html|\.htm|\.xml|\.feed|robots\.txt|\.raw|/[^.]*)$  [NC]
RewriteRule (.*) index.php



# disable the server signature
ServerSignature Off

# Enable compression
<IfModule mod_deflate.c>
  <FilesMatch "\.(js|css|php|eot|ttf|otf|svg)$">
    SetOutputFilter DEFLATE
  </FilesMatch>
</IfModule>

# Control ETags which is thought that bring better performance
<IfModule mod_headers.c>
    Header unset ETag
</IfModule>
FileETag None

<IfModule mod_headers.c>
  <FilesMatch "\.(js|css|xml|gz)$">
    Header append Vary Accept-Encoding
  </FilesMatch>
</IfModule>

<IfModule mod_expires.c>

    # Enable expirations
    ExpiresActive On

    # Default directive
    ExpiresDefault "access plus 1 month"

    # My favicon
    ExpiresByType image/x-icon "access plus 1 year”

    # Images
    ExpiresByType image/gif "access plus 1 month"
    ExpiresByType image/png "access plus 1 month"
    ExpiresByType image/jpg "access plus 1 month"
    ExpiresByType image/jpeg "access plus 1 month"

    # CSS
    ExpiresByType text/css "access 1 month”

    # Javascript
    ExpiresByType application/javascript "access plus 1 year"

</IfModule>

Thank you.

I think that if sometimes it works fast and sometimes slow, it is not that it is something wrongly configured, because in this case it would always go at the same speed.

You have to think about things that can affect you.

* Simultaneous access of many users to your website, you have to look at how many users are connected when it goes slow and when it goes fast.

* If the server is shared between several websites, it may at times not have enough data throughput, enough memory or enough processing capacity. 

But I do not understand, why my other site works like a charm with PHP 7.2 ...?

What can I do now? Do I have to make a new installation?

Hi,  nice job Chris_W and Patricia in helping out, i think you covered most of it Chris_W :)

The only thing else i can think of is that you said that both sites are with the same host, but are they on the same server as well.  If not, the other server may be a better server or configed slightly different.  Alot of hosts use servers until they are so broken they just replace them so that might be a possiblity as well.

Maybe ask your host if you can move your site to a different server.

Dont forget to also copy over your old password salt also from the old config file. If you dont then your logins wont work.

Also you could just restore the core files and not have to do a whole new install.   Also remember if you do a whole new install  you will need to reinstall all your plugins.  Before you fire up the site after the install be sure you do this or your files wont match the db for the plugins and it will blow up.

here is just the core files..

Well, thank you for all your help.

The reason was simple, my host offers simple webspace for websites. And there was my site. Now I rent a c-server and sites runs like a charm. I guess, because of more bandwidth(?)