Probably because no one else was ok with a contract for only 6 months with the risk of being sacked after 1 month.
Mazzarri if will fails next month, he will be sacked before Xmas.
Yep. It is okay with that duration of contract. It means Mazzarri must show his capability to handle Napoli in a short time. If he fails, he won't stay a long time, there will be a contract termination.
Replacing the coach for Napoli is quite the right thing at this time after seeing how Napoli had difficulty competing this season when coached by Garcia
Rudi Garcia failed to keep the good performance of Napoli. It makes sense if Napoli management decided to sack him. Napoli doesn't want to take bigger risks by keeping Garcia, they don't want Napoli position be worse. However, it won't be easy to find a proper coach, they hire Mazzari because there is no many options for the next coach.