Hi The U,
You've a long list of things there, and I can't address all of them. For some, such as your email problem, it would probably be helpful to post again with more information (who your email provider is, for example), perhaps even start a dedicated thread.
On the phone book, yes, there are a lot of fields, but if you don't fill them you won't see them except if you edit the contact. For most of mine if I click on the contact I just get a list of phone numbers and a couple of personalisation options (e.g. ringtone for that person. The placeholder for a photo is normal on android (in some views it's bigger with the HTC software than some others, but I've also seen uglier on other versions). Most of my contacts don't have photos, and while I remember this being a bit annoying when I got my first Android I don't really notice it now. I don't use FB or Twitter, and don't notice anything about them in my phonebook (there is an "updates" tab in the person details, but I only just discovered that while looking to see what annoyance I might be missing!). So I can tell you from experience that it's perfectly possible to just use this as a phonebook without any social networking stuff.
If you go into settings > apps > all you can select apps like FB and Twitter which you don't wish to use and disable them (click on the app in the list and there should be a "disable" button). If you do that they disappear from the app drawer, and the only place you'll see them is in that settings menu. That may tidy things up a bit for you.
I don't use the stock calendar app (I think I have probably removed or disabled it). There are many alternatives in the Play Store, and there are many threads about calendar apps in our
Android Applications section (search that forum for "calendar" and you'll find plenty of options and discussions). I mainly use Business Calendar, but always have at least 3 calendar apps on my phone. Which app is best depends on your tastes (e.g. I use agenda views a lot, month views rarely, so what works best for me might not be what works for you).
Similarly for messages, if you don't like the stock app there are many replacements available in the Play Store (some of which offer a lot of options for customising the appearance). Just turn off notifications in the stock app's settings so that you don't get 2 notifications for every message which arrives. I'm currently using the stock app, but with my previous phone was using Chomp, before that Pansi, before that Go SMS or Handcent. Pick an app you like, set it up how you like, then forget about it and just use it.
I've never heard of that voicemail notification issue. Hopefully someone else will have a suggestion. It could be the fact that voicemail is off that's making clearing it difficult (if the phone received the wrong signal from the network, and you can't enter the VM system to get the flag cleared because it's disabled? Just guessing here).
You don't say what system you used before, but a new platform can require a bit of adjustment, especially if you are used to things working a particular way. I find that if I make a major change (e.g. changing to a completely different ROM) I notice the things that appear worse quicker than I spot the improvements). My first rule is always to explore the settings in whatever app I'm using - remember also that a long press is equivalent of a right-click with a mouse, and often brings up other options. My second is that if the built-in app doesn't do things the way I want, there will be alternatives available that I can use instead (I use HTC's phonebook, messages and camera apps, but use alternatives for pretty much everything else).
Good luck