Log Out Button.

RE: “the logout button is the only one visible while the close button is hanging off the slider tab”
You’ll want to add some css to over ride the jigoshop style
which is effecting your close tab.
add this to your theme style file:
.login li a.close {
opacity: 1;
float:none;
}

I was also hoping to be able to remove the “dashboard” link from the slider when a customer is logged in rather than an admin if that is possible.

Sure, you’ll have to edit the file: login_panel.php
line 130 add this before the a tag:
<?php if ( current_user_can('activate_plugins') ) : ?>
and add this after the a tag line:
<?php endif ?>
This will remove the button to open the slidein panel. If that’s what you want.

Would it be possible for me to add a short amount of shortcode from another plugin that displays a customers account balance?

I believe that you can add the following probably on line #24 of the file logon_panel.php,
<?php do_shortcode([your shortcode]); ?>

HTH

well then add the css code to the superslider-login css file which will be in the folder plugins/superslider-login/plugin-data/superslider/ssLogin/( your theme)/theme.css

when adding php to a php file you need to pay attention to the php opening and closing tags.
try re-entering the code with the opening and closing php tags,
these are : <?php ?>
place the php code before the

HTH.

You seem to have the plugin deactivated at the above noted site.
If adding the css code hasn’t fixed the alignment issue, try this instead:

.login li a.close {
opacity: 1 !important;
float:none !important;
}

yep, adding apostrophes to text can be an issue. try “we are”, easiest solution.
to make the text white, add this to your plugin css, look for the rule:
#loginpanel
and add this:
color: white;
thus should work, but untill you have the plugin active I can’t check your situation. Site themes effect how to answer this question.

find the #loginpanel h2 rule and add the color:#f5f5f5 to that rule, then your h2 headers inside the login panel will be white.

#loginpanel h2 {
    color: #F5F5F5;
    margin: 0;
}

as for the close tan arrow, add this line:
position: inherit;

.login li a.close {
    float: none !important;
    opacity: 1 !important;
    position: inherit;
}

“A password will be emailed to you.”? is something that you would have to find in the actual WordPress files.
set the guest text to nothing, have you tried setting the guest text to nothing in the settings page for the plugin?