You cannot target only the video_node_form with an existing hook in D7, but you can target all node forms and then check against the node type to alter the form. Take a look at the documentation and comments on hook_form_FORM_ID_alter(). It may also help to check out how the Book module implemented this hook in D7.
function df_video_form_node_form_alter(&$form, &$form_state, $form_id) {
$node = $form['#node'];
if ($node->type == 'video') {
$form['actions']['submit']['#value'] = t('Upload');
}
}
With regard to your second question, you generally want to place your hooks in the .module file so that they are guaranteed to be picked up by Drupal. There are some cases where this is not necessarily necessary, like in hook_views_api() where you can points to a file containing other views-specific hooks.