Thanks for your question - it's quite a common concern amongst parents with children who are recovering from Kawasaki Disease!
There has been a very similar question about precautions after Kawasaki Disease that has been answered over here, including advice on contact precautions, as well as physical exertions after recovery:
Are there any precautions I need to take after my child has recovered from Kawasaki Disease?
Do follow the link for the information to most of your questions. As mentioned in the answer, the fact that your child was treated very quickly with IVIG is a good prognostic factor for complete recovery - he should be able to return to all his normal activities with time.
Regarding your specific queries about contact precautions, it would be best to follow the advice of your PD during the follow-up appointments.
We know that you may get a lot of differing opinions and "tips" from online parental forums, but it's always best to trust the advice of the doctor who is intimately familiar with all the details surrounding your child, as he will have a unique history as compared to everyone else.