How to change access callback for content create? I want to allow each user to create a specific node type only once.I know that I must use hook_menu_alter and change access callback to my own callback function.But using this way Drupal's main access callback is overriden and it will skip permissions defined in permissions page.

Is there a way to call my own access callback after main access callback is called?
Absolutely. Just replace original access callback with your own function, and then in your function do both your checks AND call the original callback function.