A few restarts on a fresh install WILL help. You will be accumulating cache files for your system, and the apps that you often use. 2 or 3 restarts MIGHT give you more comfort that your system really is working properly, so you can get to work.
What kind of major apps do you use - and are they working OK now?
Yes - I DO want to know all of that (not laughing

)
The best way to do this is to just jump right in. You may get a few TL;DR - but that's also the nature of this forum.
Just check that you don't simply repeat the same symptoms one after another. You could then just say:
This happens, and the same thing happens once every minute - or everytime I click the mouse, or every time I open a new app, or something else.
Performance issues (real draggy performance - or long pauses before something happens) are what you need to list. Which apps, how long does it happen, do you get error messages, etc.
You came here for some reason. If it is too complicated for someone else, then why did you even start by posting on this forum? Someone will help you. Maybe it's me... (I love self-flagellation

)
Well I've done already many restarts but this didn't help.
Alright, I'll start then, I'm very curious if you can handle this.

And I warned you by the way. There's a reason why I'm trying to solve this alone!
So
Problem #1)
My first issue is with Logic Pro X. You must know, this is my work computer, this is the only thing it's really used for. With Logic Pro, I have the weird issue that the spinning beach ball appears at some points. That would be when loading a project, or when quitting Logic Pro. When starting Logic, it would open up instantly, and when closing a project, as well. (at this point, it's important to know the difference between opening/closing Logic and/or a project, that's not the same)
I troubleshooted the Mac and it seems to be a core audio issue. The spinning beach ball would also appear when changing the volume output source by ALT-clicking the volume icon in the menu bar or by changing settings. None of this is normal and it hints a more serious problem.
When I turn off the core audio in Logic Pro X, the problem is gone of course, but then there's no audio so I can't play back anything. When I remove all my plugins, the problem is gone when loading a project, but not when quitting Logic Pro.
I reinstalled the Mac twice for this, but the problem is still here. Basically, everything was a fresh install. OS X was freshly installed, and so is Logic. No backups loaded, no files copied, nothing. And the problem still appears. So I thought it may be a hardware problem. But then, I wondered if I may not have installed Mavericks the wrong way, like, "unproperly", that's why I created this thread.

The installation went weirdly after all and it might still be just a software issue.
Problem #2)
I said it may be a hardware problem above. I was first thinking of the in built sound card first. When I had headphones connected to the Mac (directly, no interface) and put the volume very loud (without any audio or sound playing), I could hear weird artifacts and blips. As if something was wrong in there.
But then, the Problem #1) can't come from this, because I use an external audio interface (RME Babyface), and that would automatically bypass the internal sound card. Yet the problem (#1) is still there when the Babyface is connected and selected as the audio output. The artifacts are gone when the sound goes through the Babyface however.
Problem #3)
is that my Cinema Display (it's the 27" LED model) sometimes plays a "white noise" sort of sound through it's speakers. For a while, it used to happen every time a sound was played. Let's say I changed the volume on the keyboard, then the Mac would play the short sound that you get when changing the volume. At this point, there would be a white noise sort of sound coming from the Cinema Display, for 30 seconds or so, before it would stop. That was very weird. Now it happens not as often anymore. A problem that I believe is linked to this, is that sometimes the volume controls on my keyboard are extremely laggy, the Mac only responds much much later. And there would be no sound coming out of the Display. Apparently many users have this and a solution that helped many of them was to kill the core audio in the terminal. This never really worked for me, I think only restarting ever worked. This may be linked to the other issues.
Problem #4)
is that I get an error in the Apple Hardware Test. It says something about a Temperature Sensor Error in the PCIe bay. Some people told me this is a normal behavior for my card, that the Mac just doesn't recognize it, even though it's a Mac Edition card. (it's a Sapphire HD 7950 3 GB)
But someone else with the same Mac except in its 6 core version and the same, exact same card, didn't have this issue.
Sometimes I get grey stripes coming across the screen very quickly, very shortly. A user on here (Macinsquatch) told me this is a sign for a failing graphic card. So I will try to bring the card back as I still have warranty.
I can imagine Problem #4 being solved easily if I change my graphic card. Or at least, I hope so. But how will this affect the problems
I have no idea where to start, or what it could be. It's not easy to troubleshoot any of this.
Now I'm curious if you made it through this block of text, and if yes, if you really have a solution

So far, nobody had one. But it's okay, I try to do it alone, step by step, by asking simple questions like - Is this the correct way a OS X installation is happening? - and then I take my conclusions from this, etc. etc.
