I am curious if one is allowed to hire an illustrator to draw images for a paper (e.g. a cartoon of some chemical reaction). Should this person be included as an author or in the acknowledgements? Or is this outright not allowed?
It is entirely reasonable to hire a graphics designer or similar artist to make illustrations for scientific manuscripts, and I do in fact know people who have done so. For example, many journals now invite one to submit a "striking image" to be the splash graphic for the paper online, and this is a great place to get an artist involved.
An artist working on graphics for a paper would typically be given credit in acknowledgements but not be a co-author, since they have not made a contribution to the scientific work. There might be cases where "graphic design" might expand to become "visualization and analysis of data" worthy of an authorship, but those would likely be rare and relatively easy to distinguish.
The primary complication that this can add is one of copyright, as some journals require you to note images that need to have their copyright handled separately from the body as a whole. If you make an arrangement where the artist transfers the copyright to you, however, you can likely transfer it onwards to the journal without problem.
Seems entirely reasonable to hire an illustrator. In an ideal world, professionals who specialize in illustration would do the illustrations, freeing up researchers to do their research.
Authorship and acknowledgement seem like fundamentally cultural issues. So, it's probably best to contact the journal that you'd like to submit the paper to to ask them for guidance before hiring an illustrator.
Once you know what the journal'd require, then you might make compliance with those requirements part of the contractual terms when hiring an illustrator.
Anecdotally, I don't think that the journals I've submitted to before cared about where the illustrations came from; or, at least, they never asked. And when submitting patent applications, patent attorneys seem to have people on-staff who redraw the figures you provide them in the stereotypical rustic style that I guess the patent office expects, even when the provided figures would seem clearer and more professional.