Is exercise recommended for people who have arthritis?

Absolutely! You know how muscles get warmer and looser when you use them? So do joints. Not all exercises are perfect for arthritis, but almost any movement is better than no movement. Walking and swimming are great starts. If you choose walking, make sure you have well fitted walking shoes (try the new balance store). Yoga and tai chi are amazing for your flexibility. But always check with your provider.
Yes. Exercise is recommended for everyone able to do it. The key here is not making your arthritis worse when you exercise. Swimming is often good for people with arthritis because it's low impact, and incorporates both resistance and cardiovascular training.