upgrade issues

Your thumbs are too large, they haven’t phisically space to stay three in a row. Without change margins, you have to set your thumbs to max 280px width.
As for the space, after the thumbs will be aligned, try in CSS custom area:

.ngg-gallery-thumbnail-box {height: 50px;}

(if you display galleries always in 1 row)

Edit: This isn’t a “Nextgen thing”, but you should adjust your footer. The second line of images in the slide is shown only partially, so delete the hidden overflow or change the height.

There’s still room because that code is still not present.
Check if you have inserted it in the Custom CSS, and clear the whole cache (if you have a cache plugin, clear that too), if it doesn’t work, write:

.ngg-gallery-thumbnail-box {height: 50px !important;}

Is this ‘white space between photos and divider’ also a Theme thing?

For this and the other things, you have to test activating WP default theme and see if the issues are still present, and deactivate all plugins.

Edit 2: you also have to change the color of the title, because it isn’t visible on that dark background.