I don't know why you're having trouble with crashing and not restarting. That's certainly not typical. If an application freezes up, you can force it to quit by pressing simultaneously the apple key (also known as the command key, but that's not written on it...it's the one with the weird symbol next to an apple), the "option" or "alt" key (the key has both written on it...should be right next to the apple) and the "esc" or escape key, which I assume will be on the upper left of your keyboard (not sure if the keyboard layout on a Dutch machine is different from a US machine). That will give you a menu of all the open applications and will indicate in red any that are not responding. Sometimes one is just thinking really hard and stuck but not technically not responding...you can still force it to quit so you can unstick it. You shouldn't have to do that often unless you've installed things that are incompatible.
Why are you installing Firefox? Have you tried the Safari browser that comes with it? I don't think you really need Firefox on a Mac unless you've grown to like it (wait...weren't you the one complaining not long ago about not wanting to switch from IE to Firefox?

Did you find you like it?)
So, yeah, the volume icon thing is normal (I think you mean the one that looks like another harddrive that appears when you unzip something to install?) Once you've installed whatever is in it, you can safely drag it off to the trash (which will say eject)...it's one of those mac quirks, that to eject disks or disconnect from servers, you drag the icon to the trash...it's scary when you first switch, but at least in OS X they change the icon to an eject icon when you're actually ejecting something. It's no stranger than having to click on Start to shut down in Windows I suppose.
If you're just switching from windows, it'll take a little time to get used to everything being in totally different places, but once you're used to it, I think you'll be happy with the switch.
There are a number of mac users here, so we can help you when you can't find something.
To customize everything, play around in System Preferences, which is somewhat like Control Panel on windows...you can change the size and behavior of the "Dock" (adding and removing things to or from it is as simple as dragging the icon to it or off it...it'll make a "poof" sound when you remove something), the background, screensaver, mouse click speeds, etc.
If it's brand new and already crashing a lot, I'd call Apple Support and ask, because it shouldn't do that.