The more I study English, the more I learn about things that I doidn't know. The more I study English, the more I learn about things that I didn't know.

The past tense for know sounds better because once you've learned them, you know them :) Or, you could say, things that I don't know well. This implies that you learn more about them

I'm surprised that even the words that I already knoew can be used in a different sensecontexts. I'm surprised that even the words that I already knew can be used in different contexts.

I'm surprised that even the words I already know can be used in a different sensecontexts. I'm surprised that the words I already know can be used in different contexts.

I'm surprised that even the words I already know can be used in a different senseways. I'm surprised that even the words I already know can be used in different ways.

Today, I learned about collocations and I was surprised about the word another world. Today, I learned about collocations and I was surprised about the word another.

I'm not sure what you mean by another world

Today, I learned about collocations and I was really surprised about the another world. Today, I learned about collocations and I was really surprised.

"About another world" doesn't sound natural in this context. It would be better to say something like "really surprised" or "it was really interesting"