Thanks indianatrekker26 and SPCTRE for your tips! (Danke fuer deine Tipps!)
Regarding 'Star Trek Online' I would still like to know whether it's possible
to play parts of it offline. Thanks in advance if someone could answer this!
A broadband internet connection is required to play STO, yes. (As for payment models, they're offering 1-, 3- and 6-month subscriptions, as well as a lifetime subscription: http://www.startrekonline.com/subscribe