I like rock climbing but I am new, do you know if it's dangerous? 
Anything that requires to climb high in the air, up down, and across natural rock formations could be dangerous
Are there different skill levels? 
I do not know of specific levels, but rock climbing is physically and mentally challenging, it requires endurance agility and balance so you must start small 
I never knew it was mentally challenging. I am on the little beginners section. Any exercises I can do to improve my agility and balance?
Balance board
A balance board is a device used as a circus skill, for recreation, balance training, athletic training, brain development, therapy, musical training and other kinds of personal development.
It is a lever similar to a see-saw that the user usually stands on, usually with the left and right foot at opposite ends of the board. The user's body must stay balanced enough to keep the board's edges from touching the ground and to keep from falling off the board.
A different
rock climbers do not usually climb back down the route, or "downclimb", especially on the larger multiple pitch class III–IV, or multi-day grade IV–VI climbs. 
Rock climbing is a physically and mentally demanding sport, one that often tests a climber's strength, endurance, agility and balance along with mental control. It can be a dangerous activity and knowledge of proper climbing techniques and use of specialized climbing equipment is crucial for the safe completion of routes.
Because of the wide range