1. Rahim is being admitted into that coaching center we wanted to. —> Rahim is admitted in the future
2. Rahim is getting admitted into that coaching center we wanted to. —> Rahim is going through the process of being admitted
For the other two, the first one sounds more as if being admitted was something planned or something that you know is going to happen at a specific time, while using ‘will’ give the opposite idea of a plan, as if it’s some kind of prediction.
I hope it helps.
Regards