As early as 5 years. It has to be more fun than yoga asanas.

There are different forms of yoga. Yes at the age of 15 she can practice more dynamic form to lose weight.

Yes

It is called Astanga vinyasa or power yoga.
Twice to thrice a week is good.

Breathing exercises will help. Practices like Anulom Vilom, belly breathing etc are good.

It is a perfect age to start both breathing practices and Pranayam. These are very good tools.

All forms of yoga help with anxiety. One has to breathe in the right way while practicing.

For really younger kids it has to be with music , games, nursery rhymes they know, fun props and a very interactive teacher.
Including stretching exercises, yoga asanas focus on increasing the flexibility of the body. These help in attaining a good, taller posture. Performing yoga releases mental and emotional stress and relaxes the body. This also leads to a release of the growth hormone, which helps in increasing height.

Once the kid is ready to follow instructions you can teach them surya namaskars. But not forcibly. Yoga should be fun for kids at any age.

Yes you need to be trained to work with kids.

I started initial training at Param yoga in Aundh.

For really young kids it could be during play time. For eg Animal walks etc. You can also participate. For slightly older kids take them to a yoga class.

Blowing a feather first fast and then slow, blowing on palms and cover eyes and count 10, Counting breath backwards from 10 to 1, Lying down belly breath with toy on stomach, Mantra chanting. Play mantras every morning. These are a few ways to help kids do breathing exercises that are fun. Also, your twelve year old might be able to do Anulom Vilom.

Some basic poses like Sukhasana(cross leg), vajrasana, padmasana will help bring length in your spine. Do some twists too. This is applicable for both adults and children.

Some of the things you can do with kids with proper trained teacher:
Eye exercises, Candle meditation, Animal poses and animal sounds. Blow on closed palms and cover eyes and count 10. 5-2 4-2 3-5 sequence coordination with breath and fingers. Breathing exercises will definitely help with focus and sleep related issues. For asana practice, get him to join a proper yoga class.

The best advice I can give you is something I have tried, which is chanting. Simple OM chanting helps. You chant holding their hands too.

First you need to check strength in his/her legs. Then come up with a plan.

For kids don’t worry about too many instructions. Just breathe in from one nostril and breathe out from the other.

All standing poses in yoga. Especially Utkasana.