Does this theory homework come with a book that also teaches that theory? (One would hope so). If so, when you studied the material, did you understand what each concept meant? Or did you end up just working through exercises like you're "supposed to" without really understanding them. This may be the time to catch up to what you didn't get the first time round. See what it is that you don't know, and then go after those things. Are you doing this with a private teacher or in a class? (With a private teacher, one would hope you could ask.)
You have four five questions which also contain four five concepts. I'm guessing that they are introducing these concepts, and this exercise is for the purpose of making those concepts gel. Later on you will be working with them. So:
I. First question is about "harmonic interval". There are two concepts - 1. harmonic, 2. interval. 1. An interval is the distance between two notes. This is actually a tricky one that you should make sure you understand, because we see intervals by how they are named as well as what they are. For example CEb is a "minor third" but if you saw CD# you would call that same distance between pitches or piano keys "augmented second". Understand what "interval" means.
2. If you play a melody, then you play a note, then another note, then another note. You are going up or down from one note to the next, at a particular distance. That distance is the "melodic interval". But usually there are other notes being played at the same time. For example a melody plus chords. Or for this music you have two voices singing at the same time. One voice is higher than the other. The distance between these two voices is the "harmonic interval". "Harmonic" means the vertical part, the notes happening at the same time.
II "dissonant number". Do you understand what "dissonance" means? It's not enough to think that it is an ugly sound like CDb which would make you cringe. In that time period they had a specific idea of notes being "dissonant" that in our time we would find pleasant and acceptable. You need to find out what their definition of dissonance is.
III "beginning pitches of imitation". You have to know what "imitation" means. I haven't taken counterpoint but I can guess. Find out what imitation means. Once you know that, then you also know what its beginning pitch is.
IV "cadence" - What does "cadence" mean in general? How is a cadence identified in particular for this kind of music and analysis.
V "mode" - I've read the information on them so I have a general idea. This is probably the hardest part. Your book probably has some kind of chart or page that sets them all out for you. I would play with them and get to know them so that they are not a pile of foreign material that is abstract and you have to keep looking up from scratch. You need to understand the concept of modes in general, and then know how to recognize the modes in particular.
What resources do you have right now? How is this being taught? In a classroom or privately? Is there a textbook with it, and if so, is it understandable?
I'm not studying counterpoint right now. I went off on harmony theory and music history, after having done my rudiments. One thing I did which is very effective is that I made each concept as real as possible rather than just reading about it or memorizing definitions. If the topic was intervals, I explored them in every possible way at the piano. I looked up "interval" on the Net and listened / watched things having to do with them. If it was Early Music and instruments, I listened to the instruments, watched period dances, absorbed the sound and rhythms. The names and concepts stuck with me a lot more than in the old book study I used to do. Too often we memorize things passively and they don't stay.