I have created my own account (with a custom account type as well) to use in combination with my application but when I want to insert or edit a contact through the Address Book application on this account, it does not trigger the native activity but a custom one with just name fields...
Do you know how I can trigger the full native one instead?
It is not possible. You need to add your own Activity. One way is to add a profile action and handle it. See here: open an activity to edit contact in sync adapter.
Se also: honeycomb sync adapter features for editing contacts although there is no answer you can find useful links I found when I was dealing with it
In the example that you can find here there is only the Edit intent but it is enough to replace the action with ACTION_INSERT for the other case
