Translation:I will not study today.
I wonder if anyone has noticed another parallel: Ni is two, and hon is the counter for long skinny things (pencils, umbrellas, trees). Is it a clever coincidence that Japan = Nihon (or Nippon) = two long skinny things--Honshu and Hokkaido (plus smaller islands)? I'm just curious if that's a real thing.
Well, I see.. I didn't know saying something like "I do not study today" was weird in English. To me, using "won't" would be like saying you will make an active effort to not study (as if it's a matter of willpower). Whereas using "don't" could be interpreted as if that activity isn't scheduled for the day, or that you have made your decision and you will not study without any present or future remorse.
Don't get me wrong, it's just a slight difference I feel; and it could entirely be because English is not my first language, thus, possibly a bias from my first language, and/or the experience from learning them both.
Because it is the topic of this sentence. I was confused first too because I thought the topic meant the thing doing the action. But the definition for topic is actually "that part of a sentence about which something is said, typically the first major constituent." and in this sentence something is being said about what you are doing today. I hope this clears it up a little.
The し here is part of the verb します. To copy one of my comments from earlier:
勉強 （べんきょう）is a noun. It's turned into a verb by appending the verb する(to do). します is the polite present affirmative form of する (i.e equivalent of "I do" or "I will do"), so 勉強します= study/studies or "will study" (verb)
You'll see this happen with other nouns too, e.g. 買い物します(do shopping), or 旅行します (travel), or スポーツをします(do sports)