Where can my child have their assessment and therapy?

In the setting that your child will be most comfortable. This could be at your home or nursery/school for example.

My child is seeing an NHS speech therapist, can they see a private therapist too?

Yes :)

What does therapy involve?

Usually there will be an assessment session(s), a written report(s) and verbal feedback. With follow up therapy including ideas and activities to do at home/nursery/school.