First, those differences can be explained when you take a closer look at the variants. The J-7 was based originally on the first generation MiG-21F-13, with no airbone radar. From the MiG-21PF onwards the RP-21 'Spin Span' radar was installed into the nose, resulting in a larger intake and cone. The MiG-21 photos you are showing are MiG-21bis I suppose, which means they are of the fourth generation, with the more advanced RP-22 Jaybird radar. That F-7MG is a modified F-7 with the GEC-Marconi/LETRI Super Skyranger multi-mode radar, so we are talking here about let's say a 'third generation J-7' probably.
The other MiG-21 you show is the trainer version, I guess the MiG-21UM, which is a modified MiG-21U probably with larger fuel cell in the spine. That FT-7 was probably based on the MiG-21U, which explains the difference.
The MiG-21 and Chinese J-7 although initially a copy, went both their own ways in development. They are some exceptions in the family lines though, for example the J-7D which was based on the third generation MiG-21MF, as is clearly visible
http://www.stormpages.com/jetfight/fighter/J-7D3.jpgThat J-7FS is just an experimental modification by CAC, incorporating a larger radar antenna, and thus the intake/nosecone configuration was revised. It was probably a private venture by CAC... The 'Super-7' design also incorporating a revised intake/nose arrangement had more success, ultimately resulting in the FC-1.