If you didn't saw a difference, there are many things to consider before making assumptions, like how the software was written.
If you have background processes, like a newsletter or video encoder, you should see a difference (even with your current setup though).
1. Open to the public only what you have to. Use the command line as it will use less resources. A reason to use CPanel is if there are other managers, or it is more productive.
2. Litespeed looks promising, but I never use it so I can't advise.
3. Yes, for caching.
Also read on these topics:
1. Security, specifically on SSH access and firewall.
2. Databases (access control, backups).
3. Caching (HTTP caching if you are hosting the media and not using a CDN).
4. Timezones
Lnode and Digital Ocean have some good tutorials. There are YouTube videos as well:
https://www.youtube.com/watch?v=oFduaKmAEbg