Apache htaccess issue on modRewrite

I got an .htaccess file must to rewrite URLs for SEO friendly website,

So when i click on eg. an article ( eg www.example.com/article/this-is-an-artcle/ ) must to redirect me to index.php?article=this-is-an-article.

Same thing I must to do with the category page and admin page, so for completeness is something like this

www.ex.com/index.php?article=example-article -> www.ex.com/article/example-article   
www.ex.com/index.php?category=example -> www.ex.com/category/example
www.ex.com/index.php?page=admin -> www.ex.com/adm

Instead of this I must to hide the index.php file from the URL.

I'm doing this, but produce a 404 error

Options +FollowSymLinks

RewriteEngine On

RewriteCond %{ENV:REDIRECT_STATUS} . [OR]
RewriteCond %{REQUEST_FILENAME} -f [OR]
RewriteCond %{REQUEST_FILENAME} -d
RewriteRule ^ - [L]

RewriteRule ^article/([w-]+)/?$ index.php?article=$1 [QSA,L,NC]

RewriteRule ^category/([w-]+)/?$ index.php?category=$1 [QSA,L,NC]

RewriteRule ^adm/?$ index.php?page=admin [QSA,L,NC]

RewriteRule ^(.*)$ index.php?/$1 [L,QSA]

Unfortunately If I open the apache.err.log can't see errors relating to the RewriteEngine, so i've tried to use LogLevel alert rewrite:trace6 in my .htaccess file, but didn't produce log, also tried to put a rewrite.log file in site folder, and make 777 permissions, no change, file still blank.