Drywall thickness requirements
Thickness of gypsum board has nothing to do with upstairs or downstairs. It has to do with spacing of supports: ceilings = 1/2" on 16" on center and 5/8" on 24" on center. (A 1/2" board will sag over time from support to support if it spans too far.) 

Likewise thickness of gypsum board has nothing to do with "party walls". The Building Code requires fire wall SYSTEMS. There are many systems that use 1/2" Type X and some that use 5/8" Type X. It has to do with spacing of supports, nailing pattern, and use of insulation. 

By the way, the Building Code also requires a minimum sound rating rating in "party walls" too. Often we'll use the sound wall SYSTEM criteria as the governing criteria, and just specify that the board be fire rated (Type X) and kill two bird with one stone. 

Now, if the space is in a moist environment, (porch, steam bath area, etc.) we'll bump up the thickness for ceiling gypsum board, (I.e.: 1/2" to 5/8" thick on supports at 16" on center.)