Hope you are doing well. As described you want to publeish the PDF form where anyone who has a copy of it can fill and sign te PDF?
++ Adding to the discussion
Are you trying to publish the PDF form over the web? If yes, This is done by providing several button actions that perform functions similar to some HTML scripting macros. You must have a Common Gateway Interface (CGI) application on the web server to collect and route the data to a database. Any existing CGI application that collects data from forms (in HTML, FDF, or XML format) can be used. For more information please look at the help page: https://helpx.adobe.com/in/acrobat/using/publishing-interactive-pdf-web-forms.html