I have done BE in civil engineering. Can I pursue ME in India or abroad?

Yes ofcourse, to study further you have to meet the admission requirements which are different with different countries.

Yes, you can do this. It totally depends on your priorities from where you want to do the Master's degree in the relevant disciple, apart from this every education institute is having its different criteria to get the enrollment of the applicant in the various programmes. So kindly adhere to the adm