Is it possible to use civicrm stand alone profile page to edit existing contacts?
Generally agree with the previous commenters -- you can do an edit screen using "civicrm/profile/edit", and "webform_civicrm" is generally the next level to go if you want the effect of a standalone profile managed in a Drupal-way. There are hooks for manipulating Civi's profile screens, but they're different from the hooks of typical Drupal forms.

For completeness, we should add some links about Civi's profile hooks. The most concise reference I can think of is:


https://github.com/civicrm/civicrm-core/pull/1144/


It's a bit dense, so let's drill down on an example section:

civicrm/profile/edit:
    CSS: form#Edit .crm-profile-name-{NAME}
    Region: profile-form-{NAME}
    Hooks: buildProfile($name), validateProfile($name), processProfile($name)


What this says: If you're dealing with the page "/civicrm/profile/edit?gid=X", then there are three ways to precisely customize that profile (and no other profiles). All three require that you know the {NAME} of the profile. (This is internal name that corresponds to the DB field "civicrm_uf_group.name".)


To customize with CSS or jQuery, use a selector like "form#Edit .crm-profile-name-{NAME}". (As always, it's helpful to "View Source" and see the precise tags on your form.)
To append/prepend content programmatically, use a region named "profile-name-{NAME}".
To execute code while processing the profile, you can use hook_civicrm_buildProfile($name), hook_civicrm_validateProfile($name), or hook_civicrm_processProfile($name).


For information about other Civi hooks, see wiki.civicrm.org/confluence/display/CRMDOC/Hook+Reference . 

(NOTE: I left some links as plain-text because stackexchange limits the #links from new users.)