How to pass custom options from widget form to widget update callback?

Not sure if you’re still struggling with this, but for anyone that is, here’s the solution:

Add the following arguments to wse_widget_context_form(): $widget, $return and $instance

Then use the following to get field IDs and field names: <?php echo $widget->get_field_id('field_name'); ?> and <?php echo $widget->get_field_name('field_name'); ?> respectively. e.g.

<li><label><input value="on" type="checkbox" name="<?php echo $widget->get_field_name('noHome'); ?>" id="<?php echo $widget->get_field_id('noHome'); ?>"<?php if(isset($instance['noHome'])) echo $checked ?> />Home Page</label></li>

Hope that helps!