Your first issue is the fact that you’re on shared hosting. The fact that 1,195 websites are using the same IP address is a dead giveaway. You’re likely running into resource limits with your hosting provider.
Second is a misconception of what caching does to optimize a site. Caching helps clean up and optimize load times on the front-end of your site. None of the caching solutions you’ve talked about will be turned on when you’re logged in to your site … when you are editing pages, posts, and comments you’re running in an uncached mode and using the maximum resources available.
If you’re running this many sites on your system (it looks like you have 1 live site and 3 in-development sites) you’d be best served looking for a dedicated hosting solution. Either a real server or a VPS.
There are some potential hosting providers listed on WordPress.org. Take a look at their offerings and consider upgrading your hosting.