MarugoTabi boots Ninja Shoes Jikatabi (Outdoor tabi) MATSURI JOG 6

Are these shoes breathable, similar to sports shoes able to absorb sweat?

I usually wear a size 10.5 US / would you recommend getting the size 10 or 11 ?

Would this tabi be good for agility training outdoors, on grass or concrete? Is it secure enough in the foot to be stable for jumping and landing?

Do these run large if i wear a 12 should i get a 11 or 11.5?