Mod_rewrite (.htaccess) causing 500 server error w

I was looking for a solution on many topics (E.g. 1, 2, 3, 4, 5, 6, 7,8). Unfortunately, I did not find a good solution.

Overall, I want to achieve the following effect: no www. at the beginning of the URL, no .html or / at end of the URL, URL containing the full path to the file (but without showing its extension).

Examples: URL entered by the user >> redirection (the contents of this file should be loaded) >> address that can be seen in the address bar after redirection

www.example.com or example.com or example.com/ or example.com/index.html or example.com/index >> index.html >> http://example.com
www.example.com/abc or www.example.com/abc.html >> abc.html >> http://example.com/abc
www.example.com/abc/abc1 or www.example.com/abc/abc1.html >> abc1.html >> http://example.com/abc/abc1

File structure on my server:

 Main directory:
     index.html
     abc.html
     xyz.html
     .htaccess
     layout (there are .css, .jpg, .png ... files)
     abc:
         abc1.html
         abc2.html

My .htaccess file (version 1):

# rewrite engine initiation
RewriteEngine on

RewriteBase /

#canceling www
RewriteCond %{HTTP_HOST} ^www.(.*)$ [NC]
RewriteRule ^(.*)$ http://%1/$1 [R=301,L]

# handle trailing slashes (if not a directory)
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.+)/$ $1 [R,L]

#example.com/page will display the contents of example.com/page.html
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME}.html -f
RewriteCond %{REQUEST_FILENAME} !^.+\.html$
RewriteRule ^(.+[^/])$ $1.html

#301 from example.com/page.html to example.com/page
RewriteCond %{REQUEST_FILENAME}.html -f
RewriteRule ^(.*)\.html$ /$1 [R=301,L]

#canceling index or index.html
RewriteRule ^index.(php|html|htm)$ / [R=301,L]
RewriteRule ^([a-z0-9-_]+)/index.(php|html|htm)$ /$1/ [R=301,L]

Almost redirections work good, with the exception of these redirections:

www.example.com/abc.html >> abc.html >> http://example.com/abc (in the address bar is still http://www.example.com/abc.html)
www.example.com/abc/abc1.html >> abc1.html >> http://example.com/abc/abc1 (in the address bar is still http://www.example.com/abc/abc1.html)

My .htaccess file (version 2):

# rewrite engine initiation
RewriteEngine on

RewriteBase /

#canceling www
RewriteCond %{HTTP_HOST} ^www.(.*)$ [NC]
RewriteRule ^(.*)$ http://%1/$1 [R=301,L]

# handle trailing slashes (if not a directory)
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.+)/$ $1 [R,L]

#canceling index or index.html
RewriteRule ^index.(php|html|htm)$ / [R=301,L]
RewriteRule ^([a-z0-9-_]+)/index.(php|html|htm)$ /$1/ [R=301,L]
RewriteRule ^index$ / [R=301,L]
RewriteRule ^([a-z0-9-_]+)/index$ /$1/ [R=301,L]

#example.com/page will display the contents of example.com/page.html
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME}.html -f
RewriteRule ^(.+)$ $1.html [L,QSA]

#301 from example.com/page.html to example.com/page
RewriteCond %{THE_REQUEST} ^[A-Z]{3,9}\ /.*\.html\ HTTP/
RewriteRule ^(.*)\.html$ /$1 [R=301,L]

Now almost redirections work good, with the exception of these redirections:

www.example.com/abc or www.example.com/abc.html >> abc.html >> http://example.com/abc (I get 403 error - abc is directory, but I also have file abc.html)

...and there are several situations when I get Internal Server Error (500). This happens when I add / and any wrong characters at the end of the URL.