Help with URL Rewrite

I have the below .htaccess for my website.
What I'm expecting is that when I login to my page, I suppose to have www.example.com/myusername to be generated from www.example.com/user.php?=myusername
But that doesn't happen automatically, rather I will see www.example.com/user.php?=myusername as my browser url. But if I edit the browser url by removing the user.php?=, leaving only www.example.com/myusername and then reload, I can still access the page.
Question 1: Is .htaccess rewrite not suppose to be done automatically? I would have expected that the browser url changed to the rewrite url by itself upon login.

When I access the url www.example.com/providers/myusername, if I point the mouse to any link on the web page, for example a link with this a tag  <a href="follow_page.php?u='.$log_username.'">, I expect it to show as www.example.com/followers/myusername at the base of the page based on my htaccess rules below, rather, it shows as  www.example.com/providers/follow_page.php?=myusername and when I click the link, it shows page not found.
Question 2: Why is it showing the original url instead of the rewrite url?
Question 3: Why is it adding providers to the url?

Options +FollowSymLinks 
RewriteEngine On
RewriteBase /
# Establish a custom 404 File not found page
ErrorDocument 404 /index.php

#Prevent directory file listing in all of your folder
IndexIgnore *

RewriteRule ^(.+)/(functions|php_includes|js|images|php_parsers|sample|style|uploads|user|jssocials-1.4.0)/(.*)$ $2/$3 [L]

# Stop infinite loop
RewriteCond %{ENV:REDIRECT_STATUS} 200
RewriteRule .* - [L]

RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^([^/]*)$ /user.php?u=$1 [L]

RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^followers/([^/]*)$ /follow_page.php?u=$1 [L]

RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^providers/([^/]*)$ /provider.php?u=$1 [L]

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NOTE: In my httpd.conf file, I have:

#LoadModule foo_module modules/mod_foo.so
LoadModule rewrite_module modules/mod_rewrite.so
LoadModule dir_module modules/mod_dir.so
#

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Also

<Directory "/var/www">
    AllowOverride None
    # Allow open access:
    Require all granted
</Directory>

# Further relax access to the default document root:
<Directory "/var/www/html">
    #
    # Possible values for the Options directive are "None", "All",
    # or any combination of:
    #   Indexes Includes FollowSymLinks SymLinksifOwnerMatch ExecCGI MultiViews
    #
    # Note that "MultiViews" must be named *explicitly* --- "Options All"
    # doesn't give it to you.
    #
    # The Options directive is both complicated and important.  Please see
    # http://httpd.apache.org/docs/2.4/mod/core.html#options
    # for more information.
    #
   # Options Indexes FollowSymLinks
     Options +FollowSymLinks

    #
    # AllowOverride controls what directives may be placed in .htaccess files.
    # It can be "All", "None", or any combination of the keywords:
    #   Options FileInfo AuthConfig Limit
    #
    AllowOverride All

    #
    # Controls who can get stuff from this server.
    #
    Require all granted
</Directory>

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