Support

1. Yes, it's a good idea. These rules are generic, though. You will need to monitor your site and disable any rules which get in the way of your site's operation. There's no special configuration you need to do in Admin Tools.

2. These are different caches. Joomla's cache is about not having to go through the web application for rendering the HTML page. NginX cache is about not hitting the application and the disk at all when a resource is already in memory and hasn't expired.

Joomla's cache is a good idea as long as your site doesn't have a lot of per-user pages. For example, our site's traffic is primarily a support ticket system and the per-user pages (downloads, my subscriptions etc). It makes no sense for us using the Joomla cache since every user sees a different page anyway.

NginX cache is a good thing to enable. When to clean it? That largely depends on your site. If your site's pages and static content are unlikely to change often you could even increase that time to 8 or even 12 hours. You do have to clean it every time you update something on your site, though, be it Joomla or its extensions. There's no one-size-fits-all approach. We do use NginX as a reverse proxy on our site because of its superior HTTP/2 support and its very efficient static file management. We also use version query strings in all of our static content (JS, CSS) so we could leave the default caching behavior enabled without breaking anything on our site.

As for cPanel's cache manager... that's not a part of cPanel. Maybe it's something specific to your host. I know of some hosts which use Varnish or another caching proxy like that. Since I don't know what it is I can't tell you what to do. But I can tell you that if your site's frontend is not overwhelmingly static you will NOT benefit from it. If anything, it'd get in your way. Our host offered such a thing in the past and we had explicitly disabled it.

In so many words, the answer to each and every one of your questions is "it depends". The best way to do it is try different options and see what are the effects to your site's performance and operation.

Set the Joomla caching lower than the NginX cache timeout. Joomla uses that cache timeout setting to set the HTTP headers which tell NginX how long to cache a page (and never more than NginX's cache clear timeout). Therefore, setting a higher value in Joomla is useless.

That said, I do NOT recommend setting a very high cache time in Joomla. This will lead to stale content being delivered. The ideal setting is between 5 and 30 minutes. Enough to reduce the load on your server for very frequently visited pages, not so much as to cause stale content issues. The default of 15 minutes is a good start.