All of those things point to the server being underpowered and crashing when your site loads. When you get 'MySQL server has gone away', that means that the web server can't connect to the database server.
The only people that can help with these sort of issues are your hosting company. It's their hardware that's not handling the load, so you need to contact them. You'll either be able to have them fix it, or you'll need to move to a more powerful hosting plan that can support your site.