Okay, answer time.
1.) The shortest war was only... get this...
38 minutes. Yeah, not even as long as an episode of 'Mad Men' (or the drama of your choice). It was the Anglo-Zanzibar war in 1896 between the United Kingdom and UK-backed forces and the vast, feared armies of Zanzibar. No points for guessing who won this epic half-hour tussle. You can read more about it here
Anglo-Zanzibar war
2) As guessed by Dr Evil, the 100 years war was the longest war (at least from my reading). It actually lasted
116 years. England wanted control of the French throne and France wanted its confiscated territories back. It went from 1337 to 1453. France was the ultimate victor in this conflict, but at 116 years, no one can say England didn't put up a fight. Amazing to think a man and his great-great grandson were probably fighting in the same war at different times. You can read more about it here
100 year war.
Now, Kahran, you mentioned a 400 year war between Rome and Parthia. It's possible I'm wrong, but was it a series of conflicts about the same issue over a long period of time or a consistent state of warfare? The Crusades all had similar goals, but they still count as separate wars. Granted, the 100 year old war also had some brief truces, but they were uneasy and didn't last beyond a few years. Anyway, be interested in learning more about these ancient Roman conflicts as I don't know a lot about it.