yes running helps lean muscle but it will not necessarily make you lose it. what you should do i reduce the amount of protein you consume. If you don’t consume enough protein and enough calories, your body will cannibalize your muscles – a good safe limit is not to reduce your calories by more than 20% below your TDEE (Total Daily Energy Expenditure), to find a muscle-safe caloric intake amounts. But as for how much do you need to run thats all on you build your cardiovascular endurance first then worry about how much

Maybe 25-30 miles a week. Getting less muscle is only going to make it harder to be a gymnast though. Why not quit gymnastics? You are wanting to do something that is completely unproductive for your sport.