I do not understand the order of this sentence, why doesn't guzel go before istir?
When you have a general noun with an adjective, you must ad "bir" between the two. It is just the way things are ordered in Turkish. :)
So if memur means civil servant and memurluk means civil service, does that mean sanatcilik is a word?
Yep, it means "artistry" or "being an artist." However, it you are looking for the word for "art," it is simply "sanat" :)
(You may also see that "memur" is itself a root, but "sanatçı" is formed with a suffix)
Why not "Civil service is nice work"?