New to Showkase

(1) There is no input field to enter a themeUrl for a Juicebox gallery within the Showkase interface. However, you could simply swap the 'theme.css' file that Showkase uses for all Juicebox galleries (admin/plugins/juicebox/master/jbcore/classic/theme.css) with your own custom version.

(2) First of all, please ensure that you are using the current version of Showkase (v1.3.4) to ensure that any bugs which were present in previous versions but which have since been fixed are not contributing to your problem.
If necessary, full instructions for upgrading Showkase can be found here.
Please try viewing your gallery index page in different browsers (Chrome, Firefox, Internet Explorer, Opera, Safari) to see whether the problem is browser-dependent or is present in all browsers.
Also, please post the URL to your gallery index page so that I can see the problem for myself and investigate further.

(3) The >> is part of the Boma theme's design and it is not changeable via the Showkase interface.
If you want to hide the >>, open the admin/_themes/boma/css/styles.css file in a plain text editor and change line 539 from:

content: "\00BB";

... to:

content: " ";

After making this change, you might need to clear your browser's cache before reloading your web site to ensure that your browser fetches and uses the new version of the CSS file.

The forum's anti-spam settings restrict new users from posting links.
Apologies for the inconvenience.

More than likely. If you fire up your browser's developer tools (F12), select the 'Archive' thumbnail on your Gallery Index Page and disable the following CSS rule from line 105 of the 'styles.css' file (which limits the size of the image to ensure that layout of the page is correct):

img, object, embed {
    max-width: 100%;
}

... the image is immediately displayed larger and looks sharper.

Try changing the 'Max Thumb Columns' in 'Site -> Customize Theme -> Gallery Index Page' to see if this helps.
Choosing a different number of images to be displayed on each row will change the scale of the images and selecting '2 thumb columns' should display each thumbnail larger and this may result in it looking sharper.

Otherwise, you could perhaps upload a custom thumbnail to replace the one generated and used by Showkase in this location: /showk/_data/thumbcache/t4.jpg

Please note, though, that the thumbnails on a Gallery Index Page are not displayed at a constant size. They are dynamically resized depending on the size of the user's browser window.

You might like to look into changing the dimensions that Showkase uses to create the index page thumbnails in the source code. Try changing the default INDEX_THUMB_WIDTH and INDEX_THUMB_HEIGHT on lines 62 and 64 of the '/admin/settings/constants.php' file. Also, the function which sizes the thumbnails is the getIndexThumbSize() function starting on line 108 of the '/admin/classes/theme.php' file.
If you wanted Showkase to create thumbnails of a specific size, then you could just change line 136 of the '/admin/classes/theme.php' file from:

return array('width'=>$width, 'height'=>$height);

... to something like:

return array('width'=>400, 'height'=>300);

I do not know what knock on effects this will have (as Showkase will have no knowledge of your custom sizes) but it might be worth a try to avoid having to replace the thumbnails each time you publish your site.

Change line 13 of the '/_themes/base/pagetypes/basetheme.tpl' from:

<title dir="ltr">{$ss_siteTitle} | {$ss_navName}</title>

... to:

<title dir="ltr">{$ss_navName}</title>

Please note that the line numbers above refer to the current version of Showkase (v1.3.4).

With the Kosel theme, the second tier menu items are visible only when you are on the main page that the second tier pages are grouped under (in your case 'Main'). It is not possible to show all possible menu items at once. (For example, if you created a new gallery index page and listed several new galleries under this page, you would somehow need to have the links for all your 'Main' galleries and all your new galleries visible at the same time.)
However, the Boma theme does support this option. The Boma theme's side menu lends itself more naturally to a longer list of menu items and you can choose to always have all menu items visible at once by going to 'Site -> Customize Theme -> Navigation' and selecting the 'Show all subnav' checkbox.

With regard to your original query, if you would still rather use your own thumbnail images for your gallery index page, then you could prevent Showkase from regenerating them (and replacing your own ones) each time you publish your site by changing line 60 in the '\admin\settings\constants.php' file from:

define('OVERWRITE_INDEX_THUMBS', true);

... to:

define('OVERWRITE_INDEX_THUMBS', false);