Since I was (somehow) involved in closing every single one of these questions, it seems appropriate to say a few words.
In addition to voretaq7's excellent answer, I'll make the following observations.
First, I've written about why using a website control panel such as cPanel is a bad idea before; you may wish to read that.
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Then see What can I do when getting "Sorry, we are no longer accepting questions/answers from this account"?
To address your questions individually:
Low-traffic WordPress website on Apache keeps crashing server
I stand by the comments I made back when you originally posted the question. It sounds like you don't have the necessary skills to run your own server, and would therefore benefit from having the server management done for you. And cPanel questions are often unanswerable by this community; as professionals, it's a crutch we would simply not need or want to rely on.
http://serverfault.com/questions/443143/mod-pagespeed-using-up-too-many-resources
I marked this as a duplicate of the above question. You disagreed, and I see your point; it really wasn't a duplicate. But the rest of the community decided to close it as "not a real question" and it was automatically deleted by the system a month later.
Which Apache mods do I need on my small VPS?
This is a textbook "overly broad" question, and so "not a real question" seemed appropriate here.
http://serverfault.com/questions/443583/varnish-on-apache-and-cpanel
This is another overly broad question, asking for a step by step tutorial for installing nginx and varnish. This is totally unanswerable in its current form. This isn't really a site for posting tutorials in the first place. And actually doing this work is something that, as a professional, I would expect to invoice you for and be paid. So it's far beyond the scope of what we can reasonably do on a free Q&A site.
http://serverfault.com/questions/491250/whm-cpanel-alternatives
And I think this question ties together several of the recurring threads here.
It's "not constructive" to discuss the relative advantages and disadvantages of the control panels you listed in this question, as people are likely to engage in debate or extended discussion of even the most trivial things.
It again shows that you don't personally have the expertise to manage a server. You state that you're business people who can't yet afford to hire for this task and are looking to do it yourselves. But don't you have a business to run? If you're working on the servers, you aren't doing the things you are good at, and so you're wasting time and money.
Finally, as you move forward, I'll suggest that you keep your overall business goals in mind. Professional IT exists to support your business objectives, and as such, I strongly recommend you find someone who can do the necessary work for you on a short term contract basis, and perhaps a subscription or per-incident basis for any future maintenance that may occur. This frees you up to concentrate on building your business. Make sure you choose someone who takes the time to understand your business and proposes solutions which solve your business problems. I have a number of clients I do IT work for under this model; I may not hear from some of them for months at a time before they contact me again asking for something. Even the money you spend on a consultant can be less expensive than trying to do it yourself, if doing it yourself is distracting you from running your business.