How do I have to behave when I meet a handler and his service dog?
Do not pet! Do not touch! Do not entice!
Service dogs are like mentioned a type of medical aid, who are supposed and trained to help their handler, to cope with the impairments and disabilities they have to deal with.
If you meet someone on the street now, it is almost always the case that he is working right now:
he may be trained to watch the blood sugar level so his handler won't get into a life-threatening situation
he's protecting his human from dangereous stuff like e.g. other humans
he helps his handler at a mall and has to concentrate on his tasks
Of course it's fantastic that you like dogs too.
However, under no circumstances should you ever just touch, caress, pet or even lure an assistance dog without prior permission. Such outrageous behavior may distract the dog and you might even risk the owner's life.
"What disability do you have?"
One would think that courtesy would dictate the privacy of others, especially strangers. Unfortunately, owners of service dogs repeatedly report that they are simply approached by strangers and are brazenly asked about their disability.
It may as well be that you are just curious and just meet such a team for the first time. However, this in no way gives you the right to disregard the privacy of others.
Or would you like to impose your illness on any stranger?
Encourage the child to pet - no-go!
Of course, it's nice that your child has no fears about dogs or breaks them down with your help. But it is a no-go to send your child and ask him to pet the service dog.
Why is not it even a bit alright?
For one thing, you do not teach your child any respect for other people's property.
And on the other hand you endanger your child and the holder of the SD! Perhaps the child now distracts the dog so that he can no longer fulfill his work properly or at all and the life of the owner is therefore in danger. Furthermore his task may be precisely that he should protect his keeper from other people and shield, so he may push the little human being.
Or would you like it if someone else just touched you or your child?
Dogs aren't common property!
Everyone has the right to privacy!
"My dog also notice when I feel bad."
You do have a good relationship with your dog? That's nice. But not even remotely comparable to what it means to have a service dog at his side, let alone with the tasks he has been trained to do.
Or has your dog taken the exams and been specially trained to give you a more liveable life?
Here a german Youtube-Video on the subject.
Here two Youtube videos on the subject why you shouldn't pet SD.