Please don’t underestimate what a “basic” plugin can do. Even a simple plugin can easily cause a high server load if it’s not built properly. And if you were just making lots of changes to your website and installing software, it’s possible that this pushed you over the limit.
probably because that indicated time belongs to another time zone
yes, you can override time zone for your php / DB
but the message you are talking about came from another system that you have no influence
(system message)
The times being displayed there are the time zones of the hosting platform itself, which is not customizable. While you can change the time zone for your own website, you can set it on a per directory basis, so the system doesn’t know an “account time zone”.
Caching and CDNs help to reduce resource usage of your account, but they don’t actually help so much with entry processes and (depending on how the caching and CDN is done) may even make it worse. Website structure (how many PHP scripts are executed per page) and traffic (page views) are the most important factors.