I am replying to bullet point #2, because I am encountering the same problem:

value parameter doesn’t seem to wirk inside group fields… It has nothing to do with the select field, but with the fact that it is inside a group field.

I guess it is a problem with value, since the output of a html field inside a group field only shows the field-label, not the actual html, which is also set using value.

<?php
/*
Title: Page builder
Post Type: page
order: 1
*/

// Taken from the Piklist addons demo.

   piklist('field', array(
        'type' => 'select'
        ,'field' => 'module_selects'
        ,'label' => 'Select a Module'
        ,'columns' => 12
        ,'value' => 'module' //works!
        ,'choices' => array(
          'none' => 'Select a Module to add'
          ,'module' => 'Editor'
          ,'repeating_module' => 'Repeating Textarea'
        )
      ));

   piklist('field', array(
      'type' => 'html'
      ,'label' => 'html field label'
      ,'value' => '<i style="background-color: grey; color: #fff; padding: 5px;">HTML output</i>'
   ));

   piklist('field', array(
    'type' => 'group'
    ,'field' => 'module_group'
    ,'label' => 'Page Modules'
    ,'description' => 'Page Modules'
    ,'fields' => array(
      array(
        'type' => 'select'
        ,'field' => 'module_select'
        ,'label' => 'Select a Module'
        ,'columns' => 12
        ,'value' => 'module' //doesn't work inside a group field
        ,'choices' => array(
          'none' => 'Select a Module to add'
          ,'module' => 'Editor'
          ,'repeating_module' => 'Repeating Textarea'
        )
      )
      ,array(
         'type' => 'html'
         ,'label' => 'html field label'
         ,'value' => '<i style="background-color: grey; color: #fff; padding: 5px;">HTML output</i>' //doesn't work inside a group field
      )
      ,array(
        'type' => 'editor'
        ,'field' => 'module_editor'
        ,'columns' => 12
        ,'options' => array(
          'wpautop' => true
          ,'media_buttons' => false
          ,'tabindex' => ''
          ,'editor_css' => ''
          ,'editor_class' => true
          ,'teeny' => false
          ,'dfw' => false
          ,'tinymce' => true
          ,'quicktags' => true
        )
        ,'conditions' => array(
          array(
            'field' => 'module_group:module_select'
            ,'value' => 'module'
          )
        )
      )
      ,array(
        'type' => 'textarea'
        ,'field' => 'module_title'
        ,'label' => 'Module title:'
        ,'columns' => 12
        ,'add_more' => true
        ,'attributes' => array(
          'class' => 'large-text'
          , 'rows' => 2
        )
        ,'conditions' => array(
          array(
            'field' => 'module_group:module_select'
            ,'value' => 'repeating_module'
          )
        )
      )
    
    )
  ));