Возможно ли так настроить .htaccess?

1) пользователь видит ссылку в инете с адресом site.ru/page.php?p=123 и кликает по ней

в index.php получать $_SERVER['REQUEST_URI']

SCRIPT_FILENAME => J:/home/tools/htdocs/cgi-bin/phpinfo.php
REDIRECT_QUERY_STRING => a=b&x=y
REDIRECT_URL => /phpinfo
QUERY_STRING => a=b&x=y
REQUEST_URI => /phpinfo?x=y
SCRIPT_NAME => /cgi-bin/phpinfo.php

If you are using RewriteRule in either .htaccess files or in <Directory> sections, it is important to have some understanding of how the rules are processed. The simplified form of this is that once the rules have been processed, the rewritten request is handed back to the URL parsing engine to do what it may with it. It is possible that as the rewritten request is handled, the .htaccess file or <Directory> section may be encountered again, and thus the ruleset may be run again from the start. Most commonly this will happen if one of the rules causes a redirect - either internal or external - causing the request process to start over.

It is therefore important, if you are using RewriteRule directives in one of these contexts, that you take explicit steps to avoid rules looping, and not count solely on the [L] flag to terminate execution of a series of rules, as shown below.

The example given here will rewrite any request to index.php, giving the original request as a query string argument to index.php, however, the RewriteCond ensures that if the request is already for index.php, the RewriteRule will be skipped.