These abbreviations and meanings are expected to be known as part of the graded music exams. There is an element within the music exams where the examiner plays something on the piano and asks questions about the piece. Your child should draw on his/her knowledge of these Italian terms to answer some of the questions.
Once your child has reached exam standard and begins taking music exams he/she will need to focus not just on playing the right notes and rhythms but on musicality. Musical interpretation is important and understanding the various additional symbols on the page become more and more of a requirement.
It might be worth investing in a small music dictionary for your child. It's useful to keep in the practice area and will encourage your child to look things up for him/herself.