Absolutely. A good martial arts teacher is worth their weight in gold. The school should reflect what you want out of proper training, and the teacher should be somebody you feel your children should learn from. Kids learn discipline, respect, physical strength and confidence, and fitness. There is often wisdom thrown in, and good instructors involve parents and teachers in promotions.
Yes! Of course you need to make sure that the school is taught by someone who works well with kids, and understands that they should not be having full contact sparring! when i was 8 yrs old i started learning judo, and one of the best things it taught me was how to fall without getting hurt or hitting my head on the ground. An important skill to learn even if they choose to take up a different sport.
Yes in my opinion. Martial arts are more than exercise and generally teach respect, discipline, strategy, in addition to physical training and self defense.