* Can I use open source software under the GNU license for commercial purposes?
Yes
* Can I sell such software?
Yes
* Can I modify such software without owners permission?
Yes
* Can I sell access / membership to open source software under the GNU license or sell virtual goods created with such software?
Yes
* What legal consequences would I had to suffer if I break the license? (I live in Europe)
Same as breaking any other license, really. The GPL folks seem to try to keep an eye out for infractions, but I've never heard of them being super litigative.
Here's the catch with GPL (and other copyleft) licenses. You may sell it, modify it, use pieces of it for other purposes, use it for commercial purposes, whatever.
But if you include GPLed code in your application, it must also be released under the GPL. This doesn't mean you have to make it freely available, but it must be open source. So, when you sell it, you must either provide the source code along with the binary application, or readily provide the source code to any purchasers that request it. Further anyone that purchases an application licensed under the GPL is given the right to freely distribute it.
It gets more complex (albeit better). Just because you release some GPL code in a product, doesn't mean the whole product must necessarily be licensed under GPL. The license allows for "aggregations". What qualifies as an aggregation, what qualifies as a modification, etc. are not entirely clear. Open to debate from copyright lawyers, and open to shear mind-bending confusion from us mere mortals.
Here's the official GPL FAQ. I've always found it useful when I have questions about the GPL:
http://www.gnu.org/licenses/gpl-faq.html
Also, this page specifically deals with how Selling GPL software works, and their philosophy on it:
http://www.gnu.org/philosophy/selling.html
Personally I tend to prefer more permissive licenses, like BSD, but I can understand the logic here.
By the way, you should know, there is also the LGPL which is far more permissive, which is used for some purposes, like the standard C libraries.