Free SEO Tools
Google Pagespeed Insights
PageSpeed Insights tools does an analsis on the content of a web page and reports where improvements can be made. The report will have suggestions for where improvements can be made.
Mobile Friendly Test Tool
Google Mobile Friendly Test tool will check if your page can be seen by the mobile Googlebot. This tool also analyzes the mobile browser rendering of your site and tells you where you need to improve. This will test both mobile versions of your site and responsive web design.