.htaccess doesn't rewrite relative to the root directory - .htaccess

Question

I have tried to create an .htaccess file to do following:
Direct www.domain.com/name or www.domain.com/name/ to www.domain.com/page.php?id=name
and www.domain.com/name/2 or www.domain.com/name/2/ to www.domain.com/page.php?id=name&pg=2
my .htaccess looks like this:
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
# If the request is not for a valid directory
RewriteCond %{REQUEST_FILENAME} !-d
# If the request is not for a valid file
RewriteCond %{REQUEST_FILENAME} !-f
# If the request is not for a valid link
RewriteCond %{REQUEST_FILENAME} !-l
RewriteRule ^([a-z0-9-_\.]+)/?$ page.php?id=$1 [L]
RewriteRule ^([a-z0-9-_\.]+)/([a-z0-9]+)/?$ page.php?id=$1&pg=$2 [L]
</IfModule>
The problem is, that when I actually use a slash after name it thinks of it as a directory and looks for pages in www.domain.com/name/.. But I am still able to $_GET the variables based on id and pg.
Can anyone tell me what I have done wrong? I prefer that the URL in the address bar stays clean as www.domain.com/name/2/.
Also i have another question.. I have tried to rewrite the other URLS without luck.
If they write: www.domain.com/page.php?id=name&pg=2 and want to change the address bar URL to be be clean again, but that completely went wrong for me. Is there any specific way to do this by using what I have already made?
Thanks in advance for your help.
EDIT
The solution was based on PHP and not .htaccess. The answer was found based on this question: Stylesheet does not load after using RewriteRule and include . My problem was caused by PHP including relative to the public URL and directory. I have been forced to define a main URL variable to place before any foreign includes.

Answer 1

RewriteCond is only applicable to the very next RewriteRule.
Have your code this way:
RewriteEngine On
RewriteBase /
# If the request is for a valid directory
RewriteCond %{REQUEST_FILENAME} -d [OR]
# If the request is for a valid file
RewriteCond %{REQUEST_FILENAME} -f [OR]
# If the request is for a valid link
RewriteCond %{REQUEST_FILENAME} -l
RewriteRule ^ - [L]
# external redirect from actual URL to pretty one
RewriteCond %{THE_REQUEST} \s/+page\.php\?id=([^\s&]+) [NC]
RewriteRule ^ %1? [R=302,L]
RewriteRule ^([\w.-]+)/?$ page.php?id=$1 [L,QSA]
RewriteRule ^([\w.-]+)/([\w.-]+)/?$ page.php?id=$1&pg=$2 [L,QSA]