This professor has accepted me for an undergrad research internship in 2017. How should I stay in touch and continue our email conversations for the following months? I did ask her to send me some papers of hers and I read them. Now what should I do to continue to look interested in her research?
Well, you don't really want to start the internship now, on a remote basis. So just send an email once every three months or so with some news about yourself and your studies.
If you want to write a bit more often, that's okay too. I wouldn't write more than once a month, though.