Is it possible for children to get arthritis from cracking their joints?

Unlikely. Cracking a joint moves the parts of the joint, with the cracking noise coming from cartilage surfaces sliding, from movement of a little air-space from one place in the joint to another, or from some other non-traumatic event. A child with no joint pains before or after cracking a joint is probably not damaging the joint. However, making it a frequent habit has uncertain long-term effects.
No. Not over 10, 20 or 30 years. Over 50 or 60, possibly. A single controlled study over 50 years cracking fingers says no.