You can improve your site speed by a ton of methods, but the overall goal should be to test your site from different geo-locations using a tool like pingdom and then attend to issues. You could go for a CDN provider like Cloudflare or install caching plugins that speed up your site by reducing database queries and therefore the server load. Choosing the right hosting company for you is a critical decision and is based on many factors including your CMS, expected site traffic, and what your goals are for the site amongst others.
Of all the tools listed in this article, Moz Link explorer is an old one & quite popular. If you want to compare backlinks between two or more domains, Open Site Explorer is worth trying. This tool works best when you have a paid account of SEOMOZ though a free version of this tool is good enough to get you started checking the backlinks of your site and the sites of your competitors.