1998 Isuzu Rodeo Changed Battery Started Car Smells Electrical Burning

Can't have the battery cables connected backward if the starter worked and the engine runs. The most likely thing to be burning is the generator's output terminal. A less-than-perfect connection will result in resistance which results in heat build-up, which further degrades the connection until it really overheats. The fix for that is a replacement generator and a new terminal crimped AND soldered for a solid connection.