Does it also have extensions like redirect to old.reddit and such? If so, then it sounds like it would allow more user control than the latest versions of firefox of android, is this really true?

Yes https://apps.apple.com/us/app/oldr-redirect-for-reddit/id158...

You can also have Reddit links opened automatically in eg Apollo.

Is it also possible to make and use your own plugins?

Also I'm a bit confused that browser plugins are apps. Are they actually running as individual apps, or part of the browser?

Can they get taken down?

Yes, but I don’t know what’s like without a developer account.

All extensions are distributed as native apps, usually bundled into the primary app and are (when applicable) installed into Safari when they’re installed onto the device.

There are Content Blockers, App Extensions (into/out of Safari), Web Extensions (“of” Safari), share extensions etc with different limitations and abilities that run individually within their apps and message Safari and other apps, or have rules read ahead of time by Safari with no runtime access, or run within Safari using the WebExtension API etc etc

The archetypal web browser plug-in via the WebExtension API totally exists and are convertible for the most part to Safari’s very proprietary but very user conscious ecosystem.

https://developer.apple.com/safari/extensions/

I’m looking for a plugin where I can define my own custom mappings (via regex-like patterns). Anyone know such a plugin?

the API for content blockers is more limited, so it's not going to be as good as ublock origin, but yes, they do exist

Those extensions don't work with other browsers, though.