It is unlikely that those requirements would be held to be unconstitutional. A fundamental right such as the right to bear arms can only be restricted in specific ways ("strict scrutiny") – compelling government interest (keeping people from getting shot accidentally), being narrowly tailored and the least restrictive. If, for example, the law also required passing an exam on the history of firearms, that would be overly broad. If the registration fee were $2,000, that would be too restrictive. But the law says that
The sheriff may charge a new application processing fee in an amount
not to exceed the actual and reasonable direct cost of processing the
application or $100, whichever is less. Of this amount, $10 must be
submitted to the commissioner and deposited into the general fund.
The application fee is not just for the actual cost of applying for the permit, it also includes what looks like a $10 revenue source, and that sort of looks like an unnecessary restriction. I expect, though, that the state would argue that this $10 is necessary to defray actual long-haul expenses that could not be recovered given the $100 limit imposed by the law.
The law does not actually require a person to pay for a training course, it just requires a person to take a course (or hold employment as a peace officer in the sate within the year).