1. This depends on context. If you are saying, "On the Tuesday afternoon that I was telling you about before..." it's fine. But if you mean to say something about the coming Tuesday afternoon, then just say, "On Tuesday afternoon..." 2. I prefer the commas to separate the phrases, but sometimes commas are a matter of style, so it probably doesn't matter too much here. If this is for a class, then I would recommend looking through your notes or your textbook to see what your teacher prefers. 3. Yes. You should capitalize, but you actually need to capitalize Unit 3 and Background. Also is there a topic number? If so, put that in with a capital T for the topic, like this: The lesson that I observed was Unit 3, Topic _____: People’s Background. If there's no topic number, it seems awkward and I would make it two sentences or connect with a semi-colon. The lesson that I observed was in Unit 3. The topic was "People's Background." (In this case, I put " around the topic name because that's how we show titles of smaller portions of something else, like articles or song names, as well as a topic that is included within a unit.)