"This hotel is small."
How come in this sentence, when saying something is small, the "です" is required, but in the other examples where we were saying something was big, it was not needed?
"です" is formal. You'd use it for talking to someone you don't know or talking to someone who is superior to you. We don't have anything like it in english. You can write this sentence as "このホテルは小さい。" and it would translate the same.
no, a majority of the time you will be seen as rude if you dont use the polite form in japan
Your brain didn't have to register it is "kanji" when you read it quickly. It just registered it as a symbol you knew. You're learning. :)