Dear Iuri,
when deleting the api-browser, you should have seen a message, that you should NOT do this. The acs-api-browser package belongs to core and is an "initial-install package". Its package description does not contain a mount url, since the installer cares for this. Therefore, the package manager (acs-admin/apm) has now idea where to mount the package and how it should be set up.
However, live with OpenACS is not without hope: paste the following commands to your ds/shell,
and /api-doc will revive.
set api_browser_id \
[site_node::instantiate_and_mount -node_name api-doc \
-package_key acs-api-browser]
permission::grant -party_id [acs_magic_object registered_users] \
-object_id $api_browser_id \
-privilege read
permission::set_not_inherit -object_id $api_browser_id
all the best
-g
