Animals Still Escaping

Hello. I am still having an issue with animals escaping. I have even had horses get out from being boxed in with walls and fence gates.

Most of the time, it's my chickens escaping but also my cows and pigs. They are all surrounded by fences and fence gates. Two layers high.

Also, I can only destroy blocks with certain tools. For example, I can't dig by hand, I HAVE to have a shovel. I can't destroy anything except with the tool that does it best.

Thanks!