They do exist, and they do help. I am not one of them however, as it takes a special kind of person.
In my opinion, as long as he completes his work, its ok. Otherwise, you can offer incentives for completing his work early. Hiring a tutor to make him do his work will be a crutch moving forward.
Subject wise, yea, it would be totally ok for them to have the same tutor. However, having a the same tutor for both kids can cause issues between the kids. Having two separate tutors makes it very clear cut who works with who and when.
They have principles and superintendents for a reason. That is unacceptable behavior from a school employee, and you should complain about it.
Oh yes. But you also need to be willing to implement their strategies at home as well. Organization, time management, studying, they are all learned skills, and as such, tutors can help.
A, his classmates don't need to know. B, EVERYONE has something that they struggle with. In high school, I got A's in everything...then almost failed Spanish - in hindsight, I wish my parents had gotten me a tutor.
Autism, ding ding ding. TALK TO A MEDICAL PROFESSIONAL. PLEASE.
As someone who had the same problem, DO IT MORE. You will hate it, and you will mess it up, but in the end you will become more comfortable with public speaking.