I am a little confused about your first paragraph but I will let you know what I think of your questions...
Q: Do children have the same rights as able people?
A: Not sure what you mean by 'able people', adults maybe? But the answer regardless is yes. Every human has the same rights as every other human regardless of age/race/religion/and so on.
Q:How/when do children become able people?
A:Again I am assuming you mean adult, which here is the US is 18. In a stateless society there is no 'legal' status of 'adulthood'.
Q:Does cruelty against animals have any penalty?
A:In your scenario it appears the boy wants to/or has burned his household cat. If it's his cat, I see no 'legal' recourse by anyone to him. Although I would assume/hope his family would punish him for the cruel act. And obviously if it is someones else cat/pet animal, they would clearly have the right to go after said kid for hurting their property.
Q:The risk of property/body damage doesn't allow aggression?
A:I think what your asking is, "Doesn't the chance of the cat coming onto my property while on fire risk me and my properties well being? And therefore I have the right to stop the kid from burning the cat using aggression". (please correct me if I have misunderstood the question.) Unfortunately I don't think you have that right. Risk is daily and everywhere. Is it riskier to drive 60 in a 60 than 50 in a 50? Do you have the right when you're doing 60 in a 60 and someone else is doing 60+, to ram them off the road because there was the potential 'risk' of them hurting you by going over 60? No.

Again, please let me know if I understood your questions, properly, thanks.