I am new to android development. I just started using Parse Cloud for my android app backend. Everything works fine. Parse has option to create userids and passwords and store them securely. I can even confirm their email address by sending a activation link. The only problem is that Parse is not free completely. So is it possible to implement similar thing in google app engine without much coding like storing password securely and sending confirmation email on sign up. Here is the link that shows how Parse handles user accounts. I want to implement all options shown under Users on the link I attached.
P.S. I don't want to use (integrate) google account or facebook authentication for registration/login. I want to use my own user database containing students enroll no and their password.
No, you cannot do this with Google app engine without significant coding to manage everything.
Parse makes all of this insanely easy, so I would suggest if you're not a backend developer I would stick with Parse and worry about what happens if you get too many users later.
In the unlikely event that your app is wildly successful and you have a plan to monetize it, $200 per month shouldn't be a problem. I don't know enough about India though so maybe that's a burden. In that case, with a nicely polished app that showcases Parse's capabilities, I would be surprised if you couldn't get in touch with Parse directly and work something out.
You could also try Googling for "parse alternatives" and see what other services offer.