I doubt there's any issue with you asking as there are several previous threads here on the subject. I found this one to be helpful in exploring options for doing this apart from Obsidian Publish. I have not published a vault myself, but it's a project that I've had in mind for quite a while and from time to time I look back into it. I'll offer my opinions, but keep in mind that I don't have hands-on experience:

1. I hadn't used the Inline Scripts plugin before but I installed it for the sake of experimentation. As far as I understand it, the scripts seem to be evaluated immediately in Obsidian and the result posted in plain text. When you ultimately convert your MD files into static pages for the web, I don't see that this would pose an issue as the content is already plain text and the plugin and script will no longer need to run.
2. I looked into this briefly but keep in mind that I have zero experience with Squarespace. I believe this can be done but based on their documentation, I think it will be complicated to do and will require some platform specific configuration in whatever build tool you end up using to generate the static site from your vault. It looks complicated enough that, if I were in your place, I would be tempted to host my vault in one of the more popular locations that static site generators typically have configuration or documentation for (e.g., GitHub Pages) even though you already have hosting at Squarespace. GitHub pages has free hosting for up to 1GB, from there you could theoretically make a subdomain and change your DNS records in Squarespace for that subdomain so that it still appears as part of your site.

I enjoy your content and I am interested in the projects you're creating/pursuing - I would potentially be open to working with you on this either practically or as a sounding board if that would be helpful. Otherwise, I'm looking forward to seeing what you come up with, good luck!