Can a person suffering from arthritis do regular gym workouts?

Low impact. Aquatics, body weight, or resistance bands/ tubing biking, and/or elliptical. Aquatics allow you to perform body weight exercises, but being in water actually reduces the stress on your body due to buoyancy. Once you are able to perform body weight activities then look to add light resistance w/ bands/ tubing.
Yes. Regular exercise can help maintain range of motion. It is important to make sure that exercise does not increase swelling.