Hello and welcome to CF and to TAW.
I don't know if this will help, but I'll offer a few of my own opinions/answers.
Hello! I am a Catholic student and for my theology class I must gain insight from an Eastern Orthodox person on the following questions:
1. How do you view the Roman Catholic Church and its unity or lack of unity with your church?
I think the Great Schism was one of the most unfortunate things to ever happen within Christianity. I think it's good to consider our commonalities for the sake of charity and dialogue. But it's also important to be fully cognizant of our differences, which I find Catholics less willing to acknowledge at times than Orthodox. But to be fair, perhaps because they've only seen it from their own perspective they can't really fully comprehend what we are saying. It's not easy for an outsider to understand (I say this as a convert who had to expend substantial effort in order to shift my own mindset.).
2. What do you think of the Filioque?
I think (1) regardless of their reason for inserting it, Rome should not have unilaterally taken it upon themselves to change a foundational Christian creed, (2) History shows Rome herself was at one time opposed to changing the Creed, and (3) while I'm glad that Rome now claims an acceptable interpretation (from the Father through the Son) ... history shows that wasn't what she initially meant, and honest dialogue needs to acknowledge that fact.
3. What do you think of the teaching on Purgatory?
I don't think it's supported within Holy Tradition, nor is it a necessary doctrine from the point of view that temporal punishment of all sin is required (we don't believe that). God WILL purify everyone, but the exact mechanics of this has not been made known to us. And if time were required, it would seem counterproductive to give anyone "time off".
4. What do you think of the liturgy of the West?
I've not attended many Catholic services and can't comment. We have a Western Rite though.
5. What do you think of Rome's claim to primacy?
Rome historically had primacy. There is no debate there. The is some misunderstanding about what that means though. Primacy does not equal supremacy.
6. What do you find beautiful or distinctive about your own church?
Too many things to list.
The icons, the beauty in the Church, the chanting, the wisdom in the application to our spiritual care, the Saints and their lives, the true community that flows out of our living out the faith ...
7. What do you hope for the future concerning the unity of Christians?
I hope that the truths and the richness I have found within Orthodoxy will somehow become available to all ... but as I am also unwilling that Orthodoxy compromises or changes (as she herself resists) ... the bottom line is that all who truly learned of it would become Orthodox. I know that would upset some. To be honest, I didn't intend to become Orthodox either ... I planned to just take the parts I wanted. But it wasn't difficult to learn that what I wanted was really all of it, so becoming Orthodox became what I most wanted to be.