Where are the receiving and sending address descriptions stored? Are the sending and receiving address descriptions stored in the wallet file, or as some other file managed by the Bitcoin client app? 

If I move or copy my wallet to a new installation of the Bitcoin client, will I still have my descriptions for my sending/receiving addresses available?
Yes, all of those are stored in the wallet.dat file. I myself have successfully migrated the wallet file to a new computer and have the addresses and descriptions intact.