Smaller - Make your websites load faster
LinkChecker - LinkChecker is a free, GPL licensed website validator.
Website Grader - Grade your website's strengths and weaknesses in seconds.
Pulno - SEO Audit and Website Analysis. Pull up your SEO.
PageSpeed Ninja - One-click page speed boost for WordPress
Checkbot - Checkbot will boost the SEO, speed and security of your site by checking you're following 50+ web best practices. Browser extension with free and paid plans.