I plan to charge a small monthly (possibly yearly) fee to cover hosting, yes.

If there's demand for the front-end being open sourced, then yes. I suspect that the people who'd be willing to host the front-end would have an easier time just editing the Jekyll template YAML directly though, which is already open source: https://github.com/academicbio/academic-minima

Another option would be to allow institutions (e.g., universities, labs) to subscribe to your service to offer it to their members under their own domain name with a custom template? If you are able to interface with OAI-PMH to retrieve publication list for each author automatically from the university local repository (which they increasingly tend to have), I bet they would totally love that (as it would be an incentive for researchers to curate and update their publications list in the university repository).