Is ServerFault just for moderators? Obviously, I'm being dramatic for effect, but the moderators came off as smug, snippy and snobbish, and gave the vibe that they want to keep the site for themselves.
No. Server fault is for professional system and network administrators.
As such, we have a minimum standard for professionalism, and for the effort that we want to see to indicate that the persons asking questions are in fact professionals.
Basically the bar for questions is you must do a good portion of the troubleshooting and legwork yourself (someone even wrote a post here on about what makes a good, easily-answerable question -- oh, it was me!)you must do some of the work yourself, and that when providing answers you provide good, detailed answers that explain both the how and the why (someone even wrote a blog post about that - Google tells me it was Kyle.
I'm sorry if you feel having your questions closed was "smug, snippy and snobbish", but frankly I don't see that in the comments (though I do see some folks getting a bit exasperated), and conversely I don't see the questions as meeting our quality standards.
I've taken the time to look at each one of your questions (there were only 5, so this only took me about an hour in case you're curious) and they all have substantial flaws.
(My apologies to anyone who can't see the deleted posts, but I'm not screenshotting this stuff at this ungodly hour of the morning. Insomnia is only worth so much motivation.)
Point-By-Point
Your cPanel question
A long time ago, some blithering idiot (oh, me again) defended cPanel questions. Following my own guidelines from that defense of their existence, your question seems to be firmly chained within the bounds of the point-and-click interface, which puts you in the "User of a web application" category, not "professional system administrator".
Compounding the problem is the fact that you've told us nothing except it "keeps crashing" (refer to the aforementioned post about troubleshooting and legwork -- without some detail all you're going to get is a seething mass of loathing and hatred for cPanel...)
(Said idiot has since repeatedly and publicly said he rues the day he ever spoke those words since cPanel questions have been a fountain of crap. I'm sorry if it seems harsh, but none of our regulars seem to want to be WHM/cPanel tech support - the community consensus is they're awful products and being forced to use them is like running a marathon with your leg caught in a bear trap. If you would care to train up and be our resident expert on solving all problems cPanel we'd be happy to have you around, and you might spare some of these questions from closure, but I suspect you'd quickly come to hate them as much as we do.)
Your mod_pagespeed question
To me this really seems to be a duplicate of the cPanel question above, but with a bit more troubleshooting/research, but I'll take you at your word that it isn't.
If it is not in fact the same problem, we're back to "Inadequate troubleshooting or research has been done" based on the question. (Again, as a pro we generally expect you to do this on your own without prompting, but it's OK to forget sometimes - we know that servers falling over can be stressful. Sven was pretty gentle in his reminder.)
When you isolated the problem to mod_pagespeed you then took the discussion to the mod_pagespeed support groups (which is the Right Thing to do as you seem to have found an actual bug in mod_pagespeed -- Server Fault doesn't fix bugs in software (though sometimes we'll make suggestions for workaround). The best answer this question would have gotten based on the info I can find is "You seem to have found a bug in mod_pagespeed, you should tell them so they fix it!", which you already did).
This wasn't a bad question, just one we can't really answer because we didn't write the code.
Your "Which Apache modules should I be running" question*
Only you can prevent forest fires determine what modules should be running on your server.
If you would like someone to do a full requirements analysis for your specific environment I know that many of the regulars do consulting work (check out http://careers.stackoverflow.com to find the ones that are looking), but that kind of work is way out of scope for a simple Q&A site - (a) there's no way to do it without being in the environment, and (b) it's the very definition of "Too Localized" -- it's only useful for one specific environment.
The recommendations you got in the comments seem right on target - this is a case where you've just gotta learn some new things to do the assessment (or bring in a consultant to do it / show you how it's done).
Your "Can I use Varnish with cPanel" question
First off, "Is it possible to X
?" questions are a personal pet peeve. They invite the WORST possible answers on this site (a one-word "Yes" or "No"), and they're usually asked by someone who is omitting substantial and significant details / relevant information.
Net result, no matter how we answer that sort of question we're doing a disservice to the community (it's either a crappy one-word answer, or a bunch of guesses and assumptions that are as likely to be wrong as right).
More to the point, your question in this particular case is "If it's possible, please point me to a tutorial" -- The answer is "If it's possible Google can point you at a tutorial".
We explicitly say we don't do "learning material" recommendations in our FAQ - that includes tutorials, because an answer that is just "This is a really great tutorial ---> LINK <---" is a Bad Answer, and asking for lists of tutorials encourages people to post lots of those Bad Answers. Then when the links go dead people like me have to go through a queue of them and either fix the links or edit the answers to make sense without them. This makes us (even more) grumpy (than we usually are).
Your "What should I use instead of WHM/cPanel" question
This is a classic "Product and Service recommendation" question ("Give me a product, or list of products, that I can use in place of this other product that sucks.") -- someone should have mentioned that in he process of closing your question, including a link to that blog post which explains why we don't do those.
The Bottom Line
For what it's worth the answer to your most recent question ("What should I use instead of cPanel?") is "You should use (hire) a professional system administrator" instead of cPanel.
You're obviously bright enough to see that you're bashing your head against a brick wall with cPanel (and VPS) related problems. You're probably also bright enough to realize that the lost productivity is hurting your business.
I appreciate that your funding may not allow for a full-time sysadmin, but you can probably find someone who will work part-time for a reasonable amount of money (or a paltry sum and some equity, if your company has some obvious potential) and do the requirements analysis you seem to desperately need, and get your systems into some kind of serviceable shape that you can then maintain going forward.
Continuing to try to force your current configuration to meet your needs is basically trying to build the Taj Mahal on quicksand -- we really can't help you do that (because as professionals none of us are going to endorse a design that's doomed -- someone will come here two-three-five years later when we're looking to change jobs and find the bad advice, and it will not look good on us!).
If you ask specific, well-thought-out questions we will certainly try to answer them, but we're also not going to do consulting work for free. We have a (reasonable) expectation that when questions are asked here they'll be asked by system/network admins - that requires more (or different) technical depth than you appear to have, and imparting that much knowledge requires an apprenticeship, not a simple Q&A site.