Yes, this is fine. I did this at the end of the essay. As long as you have invested a significant amount of time, it's okay to mention projects currently underway
I talked a lot about my current research, but I have also been working on it for over a year. I think they would like to hear about it because it is what you are doing now, so by the time you matriculate, it will be an part of your as a student.
I would absolutely include current research under that section. From my experience on the interview trail, it seemed as if interviewers particularly enjoyed talking about ongoing research - it gives them a chance to talk about different potential outcomes of your work, and ask you how you would respond to each of them (e.g. If that process doesn't work, what would you try next?").
If you haven't spent much time on those projects thus far, all you really need to include is an outline of the proposed project - you will have plenty of time to fill in the details when interviews roll around.