TANCET

You can try but chances are moderate.

If your TANCET cut off range is 35 - 40. You may have the chance for Anna University.

You have chances of getting into following Colleges:
CEG - College of Engineering Guindy, Anna University, Chennai
PSG College of Technology - PSGCT
UNOM - University of Madras
SSN School of Management
St. Joseph'S College of Engineering - SJCE
Thiagarajar School of Management

You will get a nice reputation college and the best demand course in the present market, but I suggest you take only the CSE department no need of going for specializations in my view. And congratulations.

In order to take admission in ME, programs candidates have to register for TANCET counseling where they will be offered admission on the basis of their GATE/TANCET score. Admission to MBA courses will be offered on the basis of TANCET/CAT/XAT/GMAT/CMAT score.

No, it is not possible you have to first go through GATE exam or TANCET.

TANCET admission will be based on counselling and cut off decided for that particular year. All the best.

You should try for IIT Bombay, MIT manipal, VIT Vellore. This are the best college for the education and there placements are also great.

Yes, you can get MBA Admission without attending TANCET entrance exam. However, it is mandatory that you must qualify the entrance exam either conducted by the respective or other national level exam like, MAT/CAT/GMAT, etc. The admission to the MBA is based on the entrance exam score.

No, not at all it is okay if you complete it earlier. Neither of your application will get rejected.