Hello Muhanad,
I am really sorry for the delay of this reply as it is a weekend for us here.
Regarding your 2nd problem :
You can applied some hack in this file
JoomlaFolder\components\com_easydiscuss\themes\simplistic\online.php
LINE 15 until 31
<?php if( $user->id ){ ?>
<?php
$user->load( $user->id );
?>
<?php if( $user->isOnline() ){ ?>
<div class="discuss-online-status mt-5">
<i class="icon-ed-status-online" rel="ed-tooltip" data-placement="top" data-original-title="<?php echo JText::_( 'COM_EASYDISCUSS_ONLINE_SINCE' );?> <?php echo $user->getLastOnline( 'true' ); ?>"></i>
<?php echo JText::_( 'COM_EASYDISCUSS_ONLINE' );?>
</div>
<?php }else{ ?>
<div class="discuss-offline-status mt-5">
<i class="icon-ed-status-offline" rel="ed-tooltip" data-placement="top" data-original-title="<?php echo JText::_( 'COM_EASYDISCUSS_OFFLINE' );?>"></i>
<?php echo JText::_( 'COM_EASYDISCUSS_OFFLINE' );?>
</div>
<?php } ?>
<?php } ?>
Replace to
<?php if( $user->id ){ ?>
<?php
$user->load( $user->id );
?>
<?php if( $user->isOnline() ){ ?>
<?php }else{ ?>
<?php } ?>
<?php } ?>
Regarding your third question :
JoomlaFolder\modules\mod_easydiscuss_welcome\tmpl\default.php
REMOVE THIS LINE 108 until 110
<li>
<i class="ico"></i><a class="discuss-logout" href="<?php echo JRoute::_('index.php?option='.$userComponent->option.'&task='.$userComponent->logout. '&' . DiscussHelper::getToken() . '=1&return='.$return);?>"><span><?php echo JText::_( 'MOD_EASYDISCUSS_WELCOME_SIGN_OUT' );?></span></a>
</li>
Hope this help.
Best Regards
Arlex