Okay, that makes things clear.
What you can do is remove (or maybe better comment out) these lines in sources/PortalIntegration.subs.php:
$buttons = elk_array_insert($buttons, 'home', array(
'forum' => array(
'title' => empty($txt['sp-forum']) ? 'Forum' : $txt['sp-forum'],
'data-icon' => '',
'href' => $sportalurl,
'show' => in_array($modSettings['sp_portal_mode'], array(1, 3)) && empty($context['disable_sp']),
'sub_buttons' => array(),
),
), 'after');
To comment them out, you can add two consecutive / at the beginning of each line, along the lines of:
// $buttons = elk_array_insert($buttons, 'home', array(
// 'forum' => array(
// 'title' => empty($txt['sp-forum']) ? 'Forum' : $txt['sp-forum'],
ect.
to all the lines above.
Regarding the login/out, in the SP configuration page, there is an option "Disable Portal Redirection", make sure to remove the tick from it and save.