Oh no, it doesn't lists any form really, you need to figure out those yourself. I just checked the source code of this page to reply with the proper form you were asking for in your first post, I had to look for it myself
Go to the page where the action you are trying to duplicate with a button is found and try to figure out the form you would need.
For example, I don't think you can change user groups from the ModCP, but you can ban users (which perhaps is a enough for you):
<form action="{$mybb->settings['bburl']}/modcp.php" method="post">
<input type="hidden" name="action" value="do_banuser" />
<input type="hidden" name="my_post_key" value="{$mybb->post_code}" />
<input type="hidden" name="uid" value="{$thread['uid']}" />
<input type="hidden" name="banreason" value="Spammer" />
<input type="hidden" name="usergroup" value="7" />
<input type="hidden" name="liftafter" value="---" />
<input type="submit" class="button" name="updateban" value="Ban Thread Author Forever to Group 7" />
</form>
That code within the showthread* templates should work. You can even make it work for every post in the postbit* templates:
<form action="{$mybb->settings['bburl']}/modcp.php" method="post">
<input type="hidden" name="action" value="do_banuser" />
<input type="hidden" name="my_post_key" value="{$mybb->post_code}" />
<input type="hidden" name="uid" value="{$post['uid']}" />
<input type="hidden" name="banreason" value="Spammer" />
<input type="hidden" name="usergroup" value="7" />
<input type="hidden" name="liftafter" value="---" />
<input type="submit" class="button" name="updateban" value="Ban Post Author Forever to Group 7" />
</form>
Not that there are some downfalls about this. You cannot predict if the user is a moderator (can ban users) nor if the thread/post author can be banned (is a guest post) for example.
I get this code from the ./modcp.php?action=banuser&uid=X page.