After unzipping, you should find an xml file inside the root directory with the same name as the zipped file. Select the xml file and be patient because opening the file takes a little while. You can then view the data per band, or right click on the scene name to open an RGB composite.
Normally this should also work directly from the zip file.
However, you should note that the zip files are sometimes corrupted during the download, which seems to be te case with your file. In other words, I think that you are doing the right things and that the software is OK, but that the error comes from the file.
First of all I recommend to go to the official SNAP (Sentinel Application Platform - that's the real name of the software) website and get the latest version:
SNAP in some parts is still under development thus it can be that you are using an outdated version which was missing the S2 reader. After you have done that and opened SNAP go to "File->Open Product...". Now you have multiple options to open an image:
Read the main xml which is included in the .SAFE folder. should be something like S2A_OPER_MTD_SAFL1C_PDMC_20151201T155831_R121_V20151128T084811_20151128T084811.xml. 1.1 This will open all tiles included in the product. If the product contains multiple UTM zones, you have to decide which tiles you want to load (e.g. tiles from UTM35 or 36) 1.2 Additionally you can decide which resolution you want to use. You could either load all bands in their original resolution or you could resample the bands to 10, 20 or 60m
Navigate to the Granule folder included in the .SAFE folder. Here you can navigate into one of the Tile folders and select it's xml. By doing so, you can open a single tile and don't have to open all tiles of one UTM zone.