I tried to look up the information about the self-employment module but couldn't find it. It does allow a martial arts career does it not? I'm pretty sure I saw something about that before. If it's not the self-employment module, which one is it?

Anyway, I have a sim who received the Disciplined trait at birth, and I've decided I would like to have her be a martial arts instructor when she grows up. So I have a few questions as to how the career works. If she goes to the academy in her homeworld, will sims show up for her to train them? Will she receive assignments with notifications and job map tags, like for EA's professions? If she goes to China to do tournament competition, will she be paid for those? Not that I want her to, but I remember reading that sims in the career would be paid for sparring.

I've never played that career, but yes it's part of the Careers mod Self-Employed add-on module. Perhaps this FAQ and the one that follows it would be good places to start if you haven't found them yet?
Careers-SelfEmployed-FAQ#Martial-Arts

Thank you, @igazor. The page you gave me will be helpful if I change my mind about sending my sim to China for tournament competition. What I was looking for was the Interactions page, which I noticed, after following the link you gave me, are under the same link as the FAQs. But there's no listing for any of the modules. Does a page for the self-employment module even actually exist?

I guess I need to hear from someone who has actually played a sim in the martial arts career to learn how it works overall. This will be my first time ever playing a custom career, and I'd like to have some idea of what to expect before I get started.

The custom self-employed careers do not have Interactions pages. There aren't command menus associated with those. They each have at most a couple of special commands associated with them as described on the FAQ page. For example, the professional Handy Sim has the command to generate a new customer on in-game computers, but that's it. The martial arts career adds the "Challenge To a Local Ranked Sparring Match" social interaction, but again that would be about all.

What changes are the results of their actions (repairing/ upgrading things that belong to others or the town in that example) and how they are displayed on their Career tab as scores that dictate a sim's eventual leveling up.