Yes, Use the -save command. This will generate a code which can be loaded. The code will also be saved in your Warcraft III folder under Daemonic Sword/<Username> so that it can easily be copied/pasted. There are two codes: one for your character, and one for your saved stash
Can you play single Player?
Yes, the game can be played in its entirety in single-player mode.
Can you -save in single player?
Can you Cheat?
No, attempting to use a cheat code will result in you being kicked from the game.