Your cPanel questionYour 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 questionYour 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" questionYour "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" questionYour "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 FAQFAQ - 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" questionYour "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.
