Can I still use a form without embedding it to a website?

Can you use these forms internally without publishing to website? Is it okay to host web forms on JotForm?

Embedding the form on a website is just an option. You can always use the form on its standalone version by grabbing the FORM URL.

Complete guide: Where-to-Find-My-Form-URL

By default, no one knows this URL except you. So, if your intention is to keep your form private, just share the URL with the intended respondents.