Is it better to play multiple sports or focus on ONLY table tennis?
This is up to each family.  Many top table tennis players like Kanak Jha started out playing soccer or other sports.  Around age 11-12 years old, many of them decided to dedicate more time to table tennis.  Professional players usually practice around 25-30 hours/week.
 
 
What about ________   ________  US table tennis superstar who many years ago got burned out from only playing table tennis?
Actually he didn't get burned out, he went to college, got a girlfriend and turned into a party-animal.  It wasn't that he got burned out, he just got lazy and his priorities in life changed.  This had nothing at all to do with playing 1 sport or multiple sports.
 
 
How much risk is there for injury in table tennis?
Yes, without the right fitness training, warmup, and other conditioning exercises, there is a big risk of injury.  For this reason, it is important to train the entire body (including the left side) from a young age.  In the beginning, fitness isn't a huge factor to winning or losing.  However, with the right conditioning from a young age, players can have a long career without debilitating injuries.
 
 
 
Will my child be able to "fit it" at school if he is know as a ping-pong-athlete?
This is the training center's responsibility.  If the local training center can create the right environment of kids getting recognition and approval, then it doesn't matter as much what the kids at school think.  Each child must feel a sense of accomplishment and have friends within the sport.  Also, starting a school table tennis program and doing exhibitions can raise the awarness with the school as well.
 
 
Will playing table tennis 52 weeks per year lead to burnout?
Each player is different.  When I was a junior, I would take off 1-2 week twice per year.  Some players take off a month or so.  However, table tennis usually requires around 10,000 hours to reach the top level.  Too many breaks in training can lead to a loss of progress.  With a 1 month break, it will take another 1 month to get back to where they left off leading to a 2 month break.