First of all, you need to only Focus on Gate.Gate is the superset of all the exams (yeah some exams focus more on math like TIFR,ISI,CMI) .
Ans1: All psu's (except very few have own exam like ISRO) recruiting through gate.
Ans2:IIT Kanpur only through gate and IIITH have own exam after gate exam.
Ans3: Before Gate exam ==> {TIFR } ,After Gate exam ==> {JEST , ISI ,CMI ,IIITH ,BITSHD}.In all the exam mention only by jest, you are eligible for IISc Mtech research and other than that all are also good institute but not for IIT/IISC.
Gate covers more than 90% of TOP Institute and Top Psu's/ govt jobs.So only focus on GATE bcoz if you miss then you have very less no of options for entering IITs/IISc or Top Psu's .
