One arm pull ups will help, but they raise the risk of injury like pulling or tearing something. Pull ups are great for back and bicep strength, and vary from front and back pull ups, but you will also need a pushing exercise to work the triceps and chest muscles.
Absolutely, but only if you use a gradual progression of hard pullups for a very long period of time. Using bench press, bicep curl, etc, etc. will NEVER get you a one armed pullup. You can bet your life on it.
A one-hand pull-up is a good arm exercise, but you need to vary your routine. No one exercise is great over time; your body gets used to it. It is best to change exercises every few weeks. If you have free weights, these can give you both variety and results.