I could answer the first question myself. The hook I was looking for is
post_gallery (https://codex.wordpress.org/Plugin_API/Filter_Reference/post_gallery) – Whenever a gallery shortcode is getting
To consider when using this hook: The original function generating the html for galleries
gallery_shortcode() (in wp-includes/media.php) returns the new content as soon as the filter
post_gallery is used somewhere, leaving you alone with quite some work to do if you want to keep the flexibility of the original function. I highly suggest reading the original function first.
As for my second question, I still need assistance– I came up with a rather unsatisfied workaround and now use the
columns input in the gallery-settings panel on the right as my
gallery_type – Luckily for me the 9 predefined options is exactly the count of types I need.
But for the editor it's quite inconvenient and "hacky" to choose the gallery-type like this..
It's sad, because altering this panel is the only thing left on my wish-list; my
post_gallery filter is ready for a shortcode like this
[gallery ids='1,4,8' type='7']