It's more important and more efficient to understand the technical aspects of a language before you attempt to memorize a lot of different words. You will need to recall how to structure a sentence appropriately and use correct grammar a lot more than you will need to recall the word "floccinaucinihilipilification". However, I would recommend learning common phrases, reading stories/articles and memorizing words that you see frequently. Native speakers of any language will still come across words they don't know in their own language, so extending your vocabulary should be a priority only when you've mastered the basics.

When referring to paper as a material, it isn't pluralized. Yes, it is a noun but the word itself doesn't refer to a specific object. You generally wouldn't say "three steels", you would say "three bars of steel". Likewise, you would say "three sheets of paper", so you are right. However, paper has another definition. This one can be pluralized. Some documentation (such as government identification, medical records etc) are sometimes referred to as "papers". Exams are also sometimes referred to as papers. In the passage you described, they are using "paper" by this definition.

I did something similar in High School for German. I just wrote about the differences in German culture and New Zealand culture, social behaviour and stuff like that. It was actually pretty fun to write about and the teacher liked the topic. It doesn't really matter what you write about. Actually, there was this one kid in my class who wrote a My Little Pony fanfiction, so don't be that guy and you should be fine.