"I'll be teaching you English this year" is slightly more polite, firstly. It is less forceful. "I'm teaching you English this year" implies a high level of certainty. I.e. "I'm teaching you English this year, no one else, and regardless of your wishes." I am sorry every native speaker has a different story, but this is my understanding. :)

Hi! Without the context I'd say there could be a difference in meaning. The first one could mean - I'm not teaching you now but I will sometime within this year and the second one refers to an action in progress. But I think you mean them with the context that someone has already started teaching - in that case the difference is (in my opinion) of politeness. The first one seems more hopeful and open to discussion and the other one is a statement of fact. These are just my thoughts. I hope it helps :)

This is said on like a first-day situation when you meet someone for the very first time, referring to the continuous time in the future from that point forward. Essentially, you are using future continuous because you haven’t technically begun teaching yet.

Essentially the same in this context. Sorry to be very neutral about it.

You could use both in my opinion, but it does seem to imply a slight difference. "Hi guys, I'm Mr. Higgins, and I will be teaching you English this year like I have done every year." OR "Hey guys, I'm teaching English this year. Last year I taught history, but I am ready to teach something new."