WordPress permalinks is wrong. It wants me to change my htaccess file. But then site crashes

If you look at the recommended .htaccess files for WordPress, there’s a difference (yours has example.com/, whereas the recommendation is /.

# BEGIN WordPress
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteRule ^index\.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
</IfModule>
# END WordPress

I don’t know if that’s what’s causing the duplication of example.com/wp-admin/ in your URL. I suspect that is due to something incorrect in your wp-config.php file, or perhaps in your database.