Gallery links and other Page Format questions

1.
When I create a gallery, if I choose "link to Media File" then clicking on the image shows me a zoomed version of the full image, and I can then use arrows to move through the gallery. This is fine.

But I also see the option to link to an "Attachment Page". What does this mean? If I select this option, when I click on a gallery thumbnail I get the popup "loading" symbol but nothing else.

I would like an option where clicking the image loads the full-size image in a new tab. Is this possible?

2.
The various "Format" checkbox options don't seem to do anything. If I create a post as say format "standard", then change the format checkbox as "gallery", "image", "quote", "link" etc. the page doesn't change at all - it looks exactly the same. So what is the meaning of these different checkbox options?

Thanks

3.
Also with the gallery thumbnails, some images in the gallery have different aspect ratios so the thumbnail grid looks strange.
For example a square image is displayed at the same width as vertical-format images, so it has a lot of blank space below it.
I want all the thumbnails to fill the same amount of space, so it needs some "crop to fill" option, rather than what is happening now (a "zoom to fit" method").

For questions 1. and 3. I've been testing various WP gallery plugins.

NEXTGEN gallery https://wordpress.org/plugins/nextgen-gallery/
will allow adjustments to thumbnails, but also adds ugly borders around the images.

WP Gallery Custom Links https://wordpress.org/plugins/wp-gallery-custom-links/
will enable clicks to open up in a new tab, but it also breaks the next/previous functionality on the gallery page and takes you immediately to the new tab.

Of course I'd prefer to do this all without extra plugins. Is there a way with Photo theme to retain all the normal next/previous gallery functionality but simply open the full-size image in a new tab by clicking the popup image (but not automatically take you to this new tab)?

Hello,

Regarding your qestions:
1.3 - Unfortunately there's no other options, only ""link to Media File"" works properly with the popups, if you want to use default WordPress gallery, please let me know and I'll explain you how to disable gallery script.
For other functionality, please use 3rd party plugins.

2 Post Format - i.e. image post has additional image icon next to date (in single and category view), that's all.