Is there a tool that is able to brute force the private key, given a full Bitcoin address? I know it's nearly impossible, but want to try just for fun.
Yes, there is. But it was developed by the NSA and is not available to the public.
If you'd like to try to develop your own such tool, go ahead, just be aware that jack-booted thugs will show up at your door and "disappear you" if you are successful.