1) To add images to a gallery, I have to add them to the page, then delete them again so that they will only show in the gallery. Otherwise they'll show twice, as a regular image plus in the gallery. What can I do to avoid having to delete them from the page?
It sounds like you may be clicking 'Insert into post'. This is not necessary (and will include the images in the post outside the gallery). All that is required to include images in a WP-Juicebox gallery is to attach them to the post. Just drag and drop your images into the media window and after they have completed uploading, just close the media window using the cross in the upper-right corner.
2) More seriously, when expanding the gallery, the page title is not hidden but stays sitting on top of the image. What to do?
Unfortunately, there is currently a known bug whereby elements which have explicitly been assigned a CSS 'position' are not covered by the fullscreen gallery (they should be). This bug should hopefully be fixed in the next version of Juicebox.
In the meantime, there are a couple of workarounds:
(1) Set useFullscreenExpand="TRUE" (in the WP-Juicebox gallery settings interface section).
... or:
(2) Set expandInNewPage="TRUE" in (in the Pro Options text area in your gallery settings window). When the gallery is expanded, it will be displayed on a page of its own rather than on top of the embedding page. Please note that this option is available in Juicebox-Pro only (and not in Juicebox-Lite).