cannot import pictures
Exactly what happens? Please describe in detail, or show us a screen capture. If there is an error message, please quote the complete exact unedited word-for-word error message.
if I'm buying the Canon W-E1 wireless SD card adapter for the 5DSr, will it possible to do a tethered shooting inside LR
Your camera is supported for tethering in Lightroom 6.3/Lightroom CC 2015.3 or later, so I don't see what the wireless card has to do with this.
The Canon 5DSr camera is connected;
The Import Dialog shows the available pictures from the camera;
After selecting some pictures I start the import process.
The import dialog closes and the progress bar shows that LR is importing the pictures;
no picture shows up in the last import group.
after some time LR hangs. no picture was ever imported
The 5DSr runs with firmware version 1.1 but it didn't work with 1.0.1 either.
@wifi card: I mean to use the wireless connection for a tethered shooting. no cable connection.
What is the exact version number of your Lightroom? Go to Help->System Info and report the version of Lightroom shown there.
What is your exact operating system?
I don't know about wireless tethering.
Version: [6.7 1090788]
mac OS 10.22 
Secondly, if I'm buying the Canon W-E1 wireless SD card adapter for the 5DSr, will it possible to do a tethered shooting inside LR?
Highly unlikely using the standard tether tools built-in to Lightroom. They only work for wired connections. You might be able to (I don't know the software) use the Canon software to save your files automatically to a folder on your computer and to set Lightroom up to watch that folder and automatically import new files from it (check the file menu -> Auto import). That will have virtually the same effect as if you are doing wireless tethering. This is similar to when you would use an Eyefi card instead of a Canon branded card.
Jao vdL thanks for this answer, but I was aware of the possibility to use Canon EOS Utility, and a directory watch inside LR to workaraound a wireless tethering. I was interesed in the SDK support of LR for Canon, since they include the API for wireless tethering into the Canon SDK.
Unfortunately I'm still blocked from importing photos directly from my 5DSr.