The watch was important to mark twain as it showed him the correct time thus keeping him punctual. He had it working properly for 18 months until he let it run down. He had staunch faith on its judgement and its prediction. It worked perfectly until then without gaining or losing any part of it.
The Fate vs. free will in the short story can be seen as Jim makes his own decisions and doesn’t end up acting like the Sunday school books character, James, who we as the reader expect Jim to behave as. Jim has his own morals, his own personality, and he controls his fate, as anything that he can control; fate cannot.