Hello Ananta, I had a friend who was in your situation couple of years back.He chose to stay here and not finish his degree in Nepal and it was hard for him. He finished in 3 years delay with lot of struggle, financially and emotionally,
My suggestion is to go back to Nepal and finish the degree and getting masters here. If you had green card, you can stay upto 1 year but you have to file a form giving the reason for your extended stay. I don't know lot about that but I know you can stay like a year not 6 months with filing specific form. If you can't do that you can always go back to Nepal 2 times, coming back in 6 months and again going back in a month to finish another semester. Or if possible just go to give your exams and stay here rest of the time ,may be for engineering it may not be possible I guess, anyways good luck on your decision