How much dumbbells are appropriate for an 11 year old boy who has just been practicing martial arts for only a month?

Using 10 pounds of dumbbells will be fine, if they are non-removable dumbbells, such weights can be used right up to the end of junior high school.

You should be practicing traditional martial arts, then I may not be very helpful to you, because I mainly practiced Sanshou, but Muay Thai, Jiekwondo, Taekwondo, Karate, Hapkido, Judo, Brazilian Jiu-Jitsu are slightly exposed to a little bit of things, the skin of the things still know.

Beginning to exercise in the body is actually from the fourth grade, but really practicing martial arts from the junior high school. As you can see, you're focusing on flexibility now, and strength is secondary to that, and you'll get better results if you focus on strength training in middle school and high school.

Push-ups 20 a group, three consecutive groups, each group interval should not exceed 1 minute;

Sit-ups 30, three consecutive groups, each group interval should not exceed 1 minute;

Skipping rope 500, three consecutive groups, each group interval should not exceed 1 minute;

Running 800 meters minimum (you can start from 400 meters), I am every night is running 20 kilometers.

Basically this physical training is enough, the simplest is the most effective!