Hi there, welcome to the forum.
(No frameworks needed unless your app has to manage its own state).
You can use something like jQuery though to make it a little easier to access elements in the DOM. (This would not need a server)
No, you need a server to serve the page no matter what. GitHub pages will serve the page for you as a static site using a web server.
The frameworks that don’t work with static sites are server-side rendered sites or anything that needs a Node.js server (or other runtimes). Pretty much all View frameworks build out to a static site that can be run on a plain web server. “Static” broadly refers to the server not doing any runtime work (like running the JS on the server) View framework uses client-side code that will run in the browser. The site and the code are served by a web server and then the browser (the client) does all the work from then on.