Lighthouse has audits for performance, accessibility, progressive web apps, SEO, and more. You can run Lighthouse against any web page, public or requiring authentication.
You can run Lighthouse in Chrome DevTools, from the command line, or as a Node module. You give Lighthouse a URL to audit, it runs a series of audits against the page, and then it generates a report on how well the page did. From there, use the failing audits as indicators on how to improve the page.
Each audit has a reference document explaining why the audit is important, as well as how to fix it.