Hello,
Yes you can. You can change the module that it being loaded in the off canvas menu.
You can change it in your index.php file like this.
<?php if($this->countModules('matchbox_Menu')): ?>
<!-- Off Canvas Menu -->
<nav class="right-off-canvas-menu">
<a class="right exit-off-canvas">
<i class="glyph-close"></i>
</a>
<?php if(count($social)): ?>
<ul class="show-for-small list-none social-list">
<?php foreach($social as $provider): ?>
<li>
<a class="social <?php echo $provider->class; ?>" target="_blank" href="<?php echo $provider->url; ?>">
<i class="icon-<?php echo $provider->class; ?>-circled"></i><span class="visuallyhidden"><?php echo $provider->name; ?></span>
</a>
</li>
<?php endforeach; ?>
</ul>
<?php endif; ?>
<jdoc:include type="modules" name="matchbox_Menu" style="nu" />
</nav>
<?php //endif; ?>
<?php endif; // 1st off canvas navigation check ?>
to
<?php if($this->countModules('matchbox_MenuMobile')): ?>
<!-- Off Canvas Menu -->
<nav class="right-off-canvas-menu">
<a class="right exit-off-canvas">
<i class="glyph-close"></i>
</a>
<?php if(count($social)): ?>
<ul class="show-for-small list-none social-list">
<?php foreach($social as $provider): ?>
<li>
<a class="social <?php echo $provider->class; ?>" target="_blank" href="<?php echo $provider->url; ?>">
<i class="icon-<?php echo $provider->class; ?>-circled"></i><span class="visuallyhidden"><?php echo $provider->name; ?></span>
</a>
</li>
<?php endforeach; ?>
</ul>
<?php endif; ?>
<jdoc:include type="modules" name="matchbox_MenuMobile" style="nu" />
</nav>
<?php //endif; ?>
<?php endif; // 1st off canvas navigation check ?>
You should also add this position "matchbox_MenuMobile" to your configuration.php file.
As for your second request sadly this is not possible. You would have to implement a completely new and different off canvas menu.