If someone is on a visa tied to a specific job at a specific company, what is the legality of working on personal side projects (that may turn a profit)?
This is an incredibly complicated and important question and will very much depend on the facts - that is, the stage and nature of the project - because of course it's fine to think creative ideas and even execute them but the line can be crossed when this evolves into a business or a commercial enterprise. That line can be fuzzy, however.