Where: In the repository, most projects seem to use media or screenshots as the name of the directory.

How often: Whenever a big change happened or many small changes have accumulated.

What: Light theme suffices. I only care about the general look and feel, not about specific colors.

That’s how I would do it for my own projects.

That’s one option, or use imgur.

Update them if your UI has significantly changed or does not adequately represent the final product.

If having a light/dark theme is an important feature or highly requested feature for your project, it would be nice to show it off.

Screenshots can, most of the time, get away with showing just the default configuration. Share what a user would see when opening your project for the first time, and assume they used the default configuration. Optionally, if you offer a lot of customization, show what it could look like if someone spent a good amount of time personalizing things!

Yes. Git can store binary files fine. It's not the most efficient for storing them, but it works, especially for a small number of screenshots. For updating and theme, that's entirely up to you. It's all a judgement call. If you want to show off your functionality (like a dark mode), I encourage you to include screenshots of it. If you substantially change your UI, update the images.

You don't have to update for every new button you add. It's more about giving a general impression of the UI. Is it minimalist? Is it a chaotic mess? Does it look like it fits in naturally with whatever OS appears to have been used? Does it look like any thought was put into UI and UX? Those are the kinds of things you're trying to answer.