For intervals, explore the entire keyboard using intervals. Learn how intervals sound in the various ranges of the keyboard. Also try to form a connection with how an interval feels in the hand to play, how it looks on the keyboard, how it sounds to the ear, and how it may be notated on paper. The long term goal would be to develop an internalized association of the interval and all the ways it can be experienced. So for example, you see an interval on staff paper, and immediately recognize it without going to the keyboard, what the shape of then hand should be to play it, and what it sounds like in your minds ear.
Extending from above, practice singing intervals. Many university programs require proficiency in singing and keyboard as a portion of studies at the school, regardless of the primary instrument of the student. So it is very likely you will be required to sing if you gain admission to an undergraduate program. If you don't sing, IMO start now, as it is never too early to prepare for this.
In relation to intervals, sing simple melodies and begin to identify the various intervals of that melody. The long term goal would be to produce an interval by singing it, without any reference to an instrument. This would be combined with the other skills in recognizing intervals by ear, visually at the keyboard, by feel in the hand, and on paper.
Improvise with intervals, both at the keyboard and by singing. It is important to relate the study of intervals with real music. Select a few intervals, and try to improvise a piece of music around them. For example you could pick: perfect 4th and perfect 5th.
Practice transcribing music from recordings. I would advise using recordings of real music, and not just excerpts designed for theory tests. Real music would likely be more rewarding to work with, and you could use the resultant transcription to play yourself.