A plugin development framework with a lot of reusable code and a nice settings page builder.
Chill, don't panic.
My plugins that require Hikari Tools Framework aren't incomplete, they just use the Framework to do some stuff and can't work without it.
In the past I used to add the framework in each of my plugins, but that consumes extra RAM and makes maintenance very hard to be done. It's much easier to have the Framework in its own plugin and just make others require it. And that message you see is just trying to help you, explaining why the plugin isn't working and how to complete its installation.
A plugin requiring aother isn't illegal. Drupal CMS for exemple uses it a lot, and WordPress should incentive it too :)
That's also not a bad thing. In the same way a plugin requires a minimum WordPress version to work (because it uses a function that was introduced in that version), a plugin may require a minimum version of the framework.
My plugins are in constant development (as I'm able to do it for free, of course), and new features are introduced in every new version.
I suggest always keeping my plugins updated to the last version, I know how boring it is when a new version of a software is worse than older ones and I do my best to make the last version the best of them all. If for some reason you prefere an older version, just talk to me saying what was changed that you didn't like and I'll try to solve it.
That being said, always update Hikari Tools Framework first, to only then update other plugins.
Sure. Just open its file and read its source, what each method does and what parameters they receive. Get one of my plugin and see how they consume the framework, and do the same.
You'll notice the options page builder is very flexible and you can change parts of it leaving the rest untouched, and there are many methods that can be overwritten to add new sections or change existing ones.
When you publish your plugin, just inform your users that they need to install this Framework to use it. And of course, please link Hikari Tools Framework original page.
Yes, I didn't add it to my theme yet, but it can be used for side features (always keep modularity in mind: themes are meant to offer visual markup and not software features, but small features are ok), and for building theme options page.
Just be careful that, while plugins can block themselves and lay sleeping when the framework isn't available, themes must always be fully available. For that reason, in a big exception, you must check the existence of the framework as a plugin and if not found you may need to have a backup copy in the theme folder to be loaded. That's deepy discourage (I've done that for 1 year and know the problems that it creates) and should be used only on extreme situations. And when doing so, make sure to add a bright message in backend requesting user to install the framework plugin.