I'd like to ask if its possible to setup magento in a way to have one shop (same set of products, customers, payments, etc.) with two frontends?
Frontends will be configured in a way to display products with different order, positioning and promoting products for different set of customers (e.g. age range). In both frontends it shoudl be possible to buy the same products.
Whats the best approach to achieve it? Can someone recommend where to search for some hints?
Check out the multi-domain setup. I'm currently using a multi-domain setup, however both sites are completely different but share a couple cross over items, plus customer accounts work on both stores.
Check out the quick tutorial here: http://www.crucialwebhost.com/kb/how-to-setup-multiple-magento-stores/
I use the add-on domain setup, as it was best suited for my needs.
Quick note though, it mentions to copy your index.phtml & .htaccess files over, I would also recommend copying over your robots.txt file as well (with any edits needed).
If you have any questions, please feel free to ask.
You need to look at magento multi store steup. You can make additional websites and have same or different catalog of products.
Also you can make additional store views. One website may have few store views. You can specify design and some other admin configuration settings per store view or per website.
You need to try it on your devenvirioment. You can make new website and store at System->Manage Stores.