There is some great advice on accessibility at Dos and don'ts on designing for accessibility | Accessibility.
It is increasingly important to test websites on different platforms and with different browsers but once you start looking at specific devices then the permutations are huge. So use resources like Cross browser testing - Learn web development | MDN for help you and learn more. In addition Mozilla have been highlighting Free Firefox Testing on Real Devices recently (Feb 2017).
Hardening Content Security Policy (CSP) - good beginner tips
HTTP Observatory (Beta) - Mozilla Header checking
Analyse your HTTP response headers - HTTP Header Scanner
WebAIM: Alternative Text
Make the Web Work For Everyone ★ Mozilla Hacks – the Web developer blog