We are currently working on improved gallery and Splash Page sizing on mobile devices but, in the meantime, I have a couple of updates regarding your queries.
1. My site looks ok in vertical mode on an iPhone 5, but it doesn't fit the screen in landscape.
Try setting expandInNewPage="TRUE" (rather than the default value of "AUTO") in the 'General (Pro Viewers Only)' section of the Juicebox gallery page. For more information about this configuration option, please see here.
2. Is there a way to enable keyboard navigation immediately on page load?
This is possible but it requires the use of the Juicebox-Pro API and a modification to a Showkase file.
Depending on the theme you use, open the 'showkase\_themes\kosel\pagetypes\juicebox.tpl' file (changing 'kosel' to whatever theme you use) in a plain text editor and change the following code:
<!--START JUICEBOX EMBED.-->
<script src="{$ss_pageUrl}/jbcore/juicebox.js"></script>
<script>
new juicebox({
containerId : 'juicebox-container',
galleryWidth : '{$galleryWidth}',
galleryHeight : '{$galleryHeight}',
backgroundColor : '{$backgroundColor}',
baseUrl : '{$ss_pageUrl}/'
});
</script>
<div id="juicebox-container">{$ss_SEOContent}</div>
<!--END JUICEBOX EMBED.-->... to:
<!--START JUICEBOX EMBED.-->
<script src="{$ss_pageUrl}/jbcore/juicebox.js"></script>
<script>
jb = new juicebox({
containerId : 'juicebox-container',
galleryWidth : '{$galleryWidth}',
galleryHeight : '{$galleryHeight}',
backgroundColor : '{$backgroundColor}',
baseUrl : '{$ss_pageUrl}/'
});
jb.onInitComplete = function() {
document.getElementById("juicebox-container").firstChild.focus();
};
</script>
<div id="juicebox-container">{$ss_SEOContent}</div>
<!--END JUICEBOX EMBED.-->