I have the Phantom 2 Vision+ he does everything he has to do, flying, filming etc. but does not give any image on my tablet so I can't see "live" what he is doing.
Because the drone was 11 months old I returned him to DJI Germany for repair.
Their conclusion: "no warranty, water damage. new craft and gimbal".

Can someone tell me which part takes care of showing images on my tablet while the Phantom is flying and if it's possible to repair this by buying new/used parts?

You need the internal Wi-Fi unit for the Vision +.
ebay will be your best bet as apparently no dealers stock this part anymore.
DJI keep stock back for their own repair, but as they are saying water damage to the craft they only recommend replacing the whole unit as more problems could come to light with corrosion in the future.   

I think that everyone with a phantom 2 vision plus has this problem.  I believe that the wifi transmission module was shut down with a firmware update as most people report this problem after updating their aircraft.  If that is not what happened, then they were designed to fail after a short period of time, or they were so cheaply made that they would not last.  Any way you slice it DJI comes out looking like a used colostomy bag for not standing behind their product.  I started a facebook page for people with this problem to go to.  There is a petition there that you can sign.  You won't get anything from DJI, they will tell you to do a bunch of things that won't help, then say that you have to send it in at your expense, and they will repair it.  I don't trust DJI as far as I could spit a weasel.

Link to anti DJI Facebook page