IIT

You are advised to appear for GATE and score very high to get admission in M.Tech CSE at IIT.

Admission in IIT and NITs for MBA is done on the basis of CAT score.

IISc and NITs are good options for doing M.Tech beside IITs. If you are CSE or IT graduate then IIIT are equally good options for doing M.Tech.

In top IITs, the highest package offered is Rs.50 LPA, depending on your capability.

IITians with an innovative idea and solution which meets a company's competitive advantage needs can get best of International/ national salaries. For example, IITians who have their own original ideas on search engine are able to get job in Google with International salaries in the range of even one crore or more per annum.

To become an IAS officer, you need to qualify the civil services exam. For which you need to complete your graduation. IIT is an engineering institute, and to get admission in it, you need to appear for an entrance exam just after you complete class 12th (I don't know the aggregate). Both of them have a great scope. You can opt for any of them. You can appear for civil services exam after completing your B.Tech from IIT.

You may consider following options for engineering based on criterion of good placement and low fee: Delhi Technical University, Anna University Chennai, NSIT Delhi, College of Engineering Pune, Jadavpur University .

You can get job in USA after gaining few years of experience after MBA subject to visa availability. As a fresher it may be difficult to get job in USA after MBA.

Yes, I think that it would very useful if you solve old year's IIT papers. But, I also think that you should try some other questions which are related with your topics. You should also solve other entrance exams papers. It will be very useful to know which types of questions are asked in the entrance exam.
Best of luck.